Ole Rocker
I know I'm not the best person to answer these type of questions, but I'll give them a shot, so at least you'll have some additional thoughts to consider (cf Prov. 11:14).
1] Why closed communion? Why can't Orthodox Christians commune with non-Orthodox? (Oh, so that makes me a non-believer?)
The communion guidelines in Orthodoxy are, first and foremost, for the people's protection. The whole point of the Church is to help people be healed by God: it makes no sense for the Church to actively participate in what they know would harm somebody. Saint Paul says: "he that eats and drinks unworthily, eats and drinks damnation to himself, not discerning the Lord's body. For this cause, many are weak and sickly among you, and many sleep" (1 Cor. 11:29-30). Even Orthodox Christians sometimes refrain from communion if they are not "properly prepared".
Another reason that Orthodoxy has a "closed communion" is because we have maintained the apostolic practice of communing only those who are in the Orthodox Church. Can you imagine an Arian or a Marcionite going for communion at an Orthodox Church? Now, this isn't meant to compare Protestants to these groups, but the point is: where would the Church draw the line? Thankfully, this isn't something we have to grapple with, because the line was drawn by the Apostles. The apostles taught that if you aren't in the Church, you can't participate in her mysteries (or sacraments).
Communion is, in the end, not only a symbol of unity, but a real, literal communion and connection with each other. Through the eucharist, through Christ, the Church is brought together as one. (this happens by participation in other virtues such as prayer, corporate worship, etc.. but we're dealing with the eucharist just now). To partake of communion means agreement with all the dogmas of those you are communing with. In the apostolic Church, it wasn't enough to "mostly agree" on doctrine, there had to be one mind, all together believing the same thing (Jn. 17:11; Eph. 4:5; 2 Cor. 13:11; Phil. 1:27; 2:2; 1 Pet. 3:8; etc.), affirming the revelation delivered to them by the apostles (2 Thes. 2:15). Regarding those who are of a different mind, though we wish someday to have communion with them, we can't, but must as Paul said: "withdraw yourselves [e.g., the eucharist] from every brother that walketh disorderly, and not after the tradition which he received of us." (2 Thes. 3:6)
Regarding the second sentence, I'm not sure if your wife was curious about inter-communion within Orthodox churches, or whether she is asking about Orthodox Christians going to non-Orthodox churches?
2] Why chant? Isn't that rote prayer and therefore stale and abhorant to God? Why not just pray from your heart as the Protestant do? (Oh, our prayers aren't good enough?)
One might ask if saying "I love you" ever gets stale? Perhaps we should limit ourselves to once a week, or never repeat the same words? Repeating something only gets stale if you let it get stale. No matter how often we say the our Father, it will never get old or boring if we don't let it get old or boring. Every "I love you" to your wife, every "Lord have mercy" in prayer, means what we make it mean. If we simply say it with no feeling, partially paying attention, of course it's of little value (though even then it's of some value... C.S. Lewis is good at helping Protestants on stuff like this).
We find lots of examples of repeating prayers in the Bible, one of them from the Lord himself. When Jesus prayed at Gethsemane, before the betrayal, the Bible said he repeated his prayer (Mk. 14:39). And in Revelation, the prayer "Holy, holy, holy..." goes on "day and night" (Rev. 4:8; Is. 6:2-3). Another example, and one that fits in much closer to what the Orthodox do, can be seen in Psalm 136. The words "for his steadfast love endures forever" repeats 26 times in this Psalm, and in fact is repeated in every single verse.
Of course, we can pray spontaneously if we want to, though saying this is a bit of an inaccuracy. None of us really pray spontaneously, because we all have key phrases, key words, and so forth that we say when we pray. The biggest difference is that the Orthodox write down their prayers and say them, while Protestants usually just memorize certain terms and phrases and repeat them each time they pray. Both can be heartfelt, and both can be stale. And one of the reasons that we use "fixed" prayers in Orthodoxy is exactly so we can focus on our prayers and God.
It doesn't distract us or make prayer boring, it allows us to praise the Lord more freely. Rules and guideliens (and in this case, set prayers) are, as Chesterton said, the fences that keep us from going off cliffs. Written prayers of saints are protected from error (wrong belief), and confirmed by centuries of experience. They guide us more fully into the mind of the Apostles, which is the most important thing for an Orthodox Christian. It's much more important for an Orthodox Christian to conform his mind to the teachings and mindset of the Apostles, than to say prayers "the way he feels like praying".
Regarding chanting itself, the Orthodox do so because it is less open to putting our interpretations into the words. It's much easier to express our own interpretation through the tone of our voice, emphasis, etc. when we are reading than when we are chanting. Chanting, then, is used so that we get the message as it was intended, and not only as the person doing the reading understands it.
3] Why incense? Isn't this just ritual? God wants the sacrifice from the heart and all this riual becomes ... well, ritual? (Oh, that was stuff the Catholics picked up as time went on.)
Again, as with prayer, it can become just ritual if you allow it to. And just like with Prayer, Protestants (well, most of them) are no more spontaneous than the Orthodox. The difference, again, is that the Orthodox have everything written out, while Protestants go forward through the years in cycles. During each of these cycles, though, Protestant worship can become as boring and repetitive and non-heart-felt as any other group's worship.
The usage of insence is biblically acceptable to have while worshipping God (Rev. 8:3; Lk. 1:10). Malachi says: "For from the rising of the sun even unto the going down of the same my name shall be great among the Gentiles; and in every place incense shall be offered unto my name, and a pure offering: for my name shall be great among the heathen, saith the Lord of hosts." (Mal. 1:11). In this Scriptural passage, incense is seen not as something that hinders true worship, but as something that happens right along with "a pure offering".
But why? Do we Orthodox do it just because the Bible talks about it, or just "cause it's tradition"? The answer to this (and the answer to this question any time it's asked), is no, we have specific reasons for why we do what we do. In the case of incense, there is a very important reason, IMO, for using it. In Orthodox theology there can sometimes appear to be a body/soul dualism, that makes the body seem like a prison that we need to be set free from. Many monastic texts give this impression, and many times new converts can get this from the strict asceticism promoted in Orthodoxy.
So how does incense play in then? It reminds us that the body is good. That we are to use our bodily senses, and that our bodies not only can, but must be part of our worship of God. Man is not soul alone: the body is a crucial part of him:
'God gave independent being and life neither to the nature of the soul by itself, nor to the nature of the body seperately, but rather to men, composed of soul and body, so that with these same parts of which they are composed, when they are born and live, they should attain after the termination of this life their common end; soul and body compose in man on living entity.' There would no longer be a man, Athenagoras argues, if the completeness of this structure were broken, for then the identity of the invidiual would be broken also. - Georges Florovsky, Creation and Redemption: Volume 3 of the Collected Works, (Nardland, 1976)
We Orthodox, even as we fast and prostrate and hold vigils and a great deal more, always hold the body as something to be cherished, and something that can lead us into a closer relationship with God. God himself is immaterial, but in our present state, the body is very important in helping us to reach to God. It's not totally accurate to say that "God is spirit, so we should meet him in spirit". God is spirit, but compared to him, even our spirits and souls (even the angels) are material. (This isn't to say that they are material. Yet, in comparison with God, who alone is uncreated, they fall, to some degree, short of immateriality).
The Orthodox usually try to involve the body in whatever they are doing. We don't worship God with one aspect of ourselves (e.g., spirit), but worship him with our whole bodies. So, we use things like incense, processions, candles, etc. to bring our senses--our bodies--alive, and make help them participate more fully in the service. Incense, then, in the end, can be thought of as a method for bringing us into closer communion with God.
4] How is it right to say to the Theotokos "I put my whole trust in you, Thou who protects me" or something along those lines? (This is blatant idolatry!)
This is a topic all to itself! First, if she doesn't believe that angels and saints intercede for us with their prayers in heaven, then there's really not much that can be said. I'll try to run through the basic arguments for that real quick, but that's really a subject that a Priest should go into some depth in explaning (if you could get your wife to meet with one 
... maybe invite a Priest to your house? unless she would see that as an invasion of her space?) I'd first go over all the stuff about intercessory prayer, (Eph. 1:16; Col. 1:9; etc.) and try to help her understand that there is a difference between intercessor and mediator: the bible says there is one mediator, not one intercessor. (1 Tim. 2:5)
Essentially, the Orthodox believe that our God "is not the God of the dead, but the God of the living" (Mark 12:26-27; Luke 20:37-38). The Orthodox therefore see the "great cloud of witnesses" in hebrews (12:1, 22-24) as being the saints in the "Church triumphant". (this is exegetically consistent considering that the whole previous chapter was talking about the saints of God from the past who had remained faithful). The reason that Paul had such a strong "desire to depart, and to be with Christ; which is far better" (Phil. 1:21-24; cf 2 Cor. 5:1-9) is because he knew that he wouldn't be "sleeping" for millenia, but would be with Christ "in paradise that day" (cf Lk. 23:43).
Perhaps the clearest biblical evidence of saints being in heaven can be seen in the Apocalypse of John. Indeed, if you read through it you'll see numerous allusions--and sometimes explicit passages--regarding the saints being alive in heaven. Here's an example: "When he opened the fifth seal, I saw under the altar the souls of those who had been slain because of the word of God and the testimony they had maintained. They called out in a loud voice, "How long, Sovereign Lord, holy and true, until you judge the inhabitants of the earth and avenge our blood?" Then each of them was given a white robe, and they were told to wait a little longer, until the number of their fellow servants and brothers who were to be killed as they had been was completed." (Rev. 6:9-11; cf 7:9-17; 8:3-4)
The Orthodox believe that "neither death nor life will be able to separate us from the love of God," (Rom. 8:38-39; cf Rom. 14:8-9), and we believe that death cannot separate us from experiencing that love in a real, actual way. As a last note on the biblical evidence, for some passages regarding angels interceding for us, see: Tob. 12:12-15; Zec. 1:12; Heb. 1:14; Ps. 91:11; Matt. 18:10.
The early Church believed that the saints were indeed alive in heaven, and could pray. It was said, for example, that christians pray "in the society of angels, as being already of angelic rank, and he is never out of their holy keeping; and though he pray alone, he has the choir of the saints standing with him [in prayer]" (Clement of Alexandria, Miscellanies 7:12) and that: "not the high priest [Christ] alone prays for those who pray sincerely, but also the angels...as also the souls of the saints who have already fallen asleep" (Origen, Prayer 11). We see this pattern in almost every Church Father after the 3rd century, and even a few (some mentioned above) before the 4th century.
If this is understood and accepted, the Orthodox view of Mary becomes easier to understand. When we say we put our trust in the Mother of God, we mean that we know she will pray to God for us, and that her prayers have power. Just like Paul prayed for others, we also ask the saints in heaven to pray for us, and trust that they will protect us (in Orthodox theology, we also each have a guardian angel, but that's another topic).
One main sticking point with accepting this is misunderstanding how we are saved. Certainly we are saved by God, by Christ; however, it is possible for God to use people, events, things, etc. as instruments for bringing someone to salvation. For instance, in James we find the words: "Brethren, if any of you do err from the truth, and one convert him; Let him know that he which converteth the sinner from the error of his way shall save a soul from death, and shall hide a multitude of sins" (James 5:19-20). We find something similar in the Apostle Paul: "Take heed unto theyself and unto the doctrine; continue in them: for in doing this thou shalt both save thyself, and them that hear thee" (1 Tim. 4:16).
James and Paul, of course, do not mean that we have the power to save anyone in and of ourselves. In the same way, the Orthodox do not see Mary as some type of demi-God who can save us by her own power. However, the Orthodox do believe that people, and saints in heaven, can have an effect on what happens in the world. We don't make an idol our of Mary, we simply recognize that her prayers have great powers and that we can have faith that she will intercede for us if we ask her. In the end, though, all Orthodox say: "The Lord's will be done".
One final note, it might be helpful to explain that in Orthodox thought God is so totally other it's mind-boggingly incomprehensible. Mystery, apophaticism, awe, and the christological and trinitarian discussions in the early Church all point to how awesomely different and incomprehensible and other God is. When we talk about saints, and the Theotokos, our words must be understood in this context. You can't take them out of their context and view them fairly.
5] Why all the long ritual over the blessing of the Eucharist? Why not a quick "finger-waving" and then serve it? Why all the fuss over every little crumb and drop?
Because the eucharist is Christ in a very real way. How would we act if Christ were here with us today? Would we do a "quickie service" and do a quick bow and say "Great seeing you Jesus! talk to ya next Sunday"? Of course, we would make quite a fuss over Him being there. We would be in awe. We would take our time and do things right. We would want everything to be perfect in honor of him. This is the way we are to approach the liturgy, because Christ Himself has offered us the wonderful gift: the eucharist, the body and blood of the God-man. That's why the fuss, and that's why we take our time
Justin
PS. Please forgive the length, I find it hard to summarize such subjects in a few words.
