Welcome to the forum
Some thoughts (and take everything I say with a grain of salt, I'm just a recent convert myself)...
2) Does the Orthodox Church believe in the concept of
mortal sin as does the Catholic Church? If so, are there
any differences between what the Orthodox Church
sees as mortal sin and what the Catholic Church sees
as mortal sin?
I think this depends largely on who you ask (ie., there is no one position that is "right," but there are a number of acceptable perspectives). In America today (and I assume in the west in general), Orthodox Priests tend to distance themselves from what they perceive to be "Roman Catholicism," and because of this you will hear many say that "Orthodoxy doesn't give penances such as saying 10 Hail Mary's," that "Orthodoxy doesn't divide sins into categories," and so forth. This is at best misleading. Church history clearly shows that Orthodox Priests did in fact give penances in past times unlike what they would give today (e.g., if you masturbate you might have to do 12 prostrations a day, with appropriate prayers, and not partake in communion for 40 days). Today the Orthodox seem to shy away from words and practices like that, which I assume is an allowance for our weakness. I do think the Orthodox view overall is different, so in a way I can understand the change in language; I think it important to admit that there are "moral sins" though. Regarding the actual sins (whether you call them mortal or not), I think we are pretty close to Catholicism.
3) I know the Orthodox Church does not believe in the
false doctrine of once-saved-always saved. So, how
does someone in a state of grace lose that grace?
Is it mortal sin?
I think the quickest way to explain it would be to compare it to a patient receiving medicine. The medicine had the ability to save from the beginning, no one denies that it was potent enough from the beginning and sufficient enough to save someone. So a person starts participating with this medicine (God's grace), and starts to get better. If, however, the patient later decides to stop taking the medicine, the physician doesn't force him to continue taking it. Certainly he and those around him try to persuade him, but they don't make him do something he doesn't want to do. Maybe he had been healed enough that he will live. Maybe he'll relapse after a little while. There's no real way of knowing. All that is known is that the medicine saves, and that we need to focus on taking it for all our lives. There's never a point at which we can proclaim ourselves healed and no longer in need of God's medicine (grace).
Regarding the "how," I think you can turn away in many many ways, though only the bigger ones can prevent your receiving the medicine. For instance, if someone cuts you off in traffic and you snap at them, you will be hindering God's grace; you're creating an atmosphere where the passions reign and God's love doesn't. This in itself is minor, but if it builds up further and you get mad all day, holding a grudge and wanting revenge, then all of a sudden God's grace is being almost totally blocked out. In that way, while there are distinctions between the different levels of sin, all sin is treated as wrong and all sin needs to be repented (even sins you did out of ignorance).
4) What about contraception and the Orthodox Church?
I understand that some Orthodox see it as wrong and
others do not. For those who see it as wrong, is it
considered a mortal sin?
I think this is largely between you and your Priest (and God, of course!). I can't say whether it's mortal or not; I do think it's wrong though. In fact, I don't think Orthodoxy will, in the future, condone the use of contraceptives as widely as they do now (if at all). I disagree with most of what Catholic apologist Dave Armstrong says, but I think he's right on this issue, the currect Orthodox position (in some places, like America) on contraception is a moral lapse and not in line with either biblical or patristic thought. I look forward to the day when it's usage is extremely rare, and then only with NFP being used. (I don't consider NFP to be wholly valid either, I think it's contraception too, it's just a lesser evil than other forms on contraception).