1.) In the Orthodox Church, are we able to approach communion with unconfessed sins? I know there is no distinction between venial and mortal as in the RCC, and so we must confess all of our sins, voluntary or not. At the same time, it seems that if we must confess every single sin we commit before taking communion that we would never be able to approach the chalice. My priest says we should commune frequently, but every time I sin in between confession and the Divine Liturgy, I feel like I shouldn't approach.
Strictly speaking, the only sins that would prohibit someone from receiving Communion without having first confessed are particularly grievous sins which "automatically excommunicate". I'm not sure what the lower threshold of this category is, but murder, adultery, apostasy, fornication, and the like are some of these. Ask your priest/confessor. I tried asking in another thread, but there were no takers.
So, presuming that the sins in question are not of this level of seriousness, it would be acceptable, even desirable (required?) to commune at the Liturgy, if otherwise prepared.
2.) If we do not do not fast on Wednesday and Friday, are to abstain from communion? I come from a fairly irreligious family (though nominally Orthodox) and while I've heard of fasting on Saturday night, I actually haven't heard of the Wednesday and Friday fast being important until recently. I've also taken communion before without fasting on Wednesday and Friday and now I feel bad.
Don't feel bad about the past.
Generally, I would say yes, the Wednesday and Friday fasts are "required" and are part of our preparation for Communion in a broad sense. But I don't recall having ever seen anyone turned away from the chalice for this reason because a) there are no "Fasting Police" spying on communicants during the week, and b) the origin and reason for the W/F fast has nothing really to do with Communion.
3.) I know fasting is important but I've also heard it said that though we fast from food the real fast is from sin. So the question I have is what the relationship between the two is? How does exercising one lead to the conquering of the other? I'm not doubting its efficacy, but some Protestants say we don't need to fast, though I'm sure there is a good reason.
This has been discussed before, so I'd encourage you to search the old threads. To be very brief, we sin in the body as well as in the soul/spirit, so we repent in the body as well as in the soul/spirit.
As for the Protestants who say we don't need to fast, their argument is with the Lord, not with us.