I remembered!!! I have a New Oxford Annotated Bible from college; it has the deuterocanonical texts, which I'd like to read. It's an NRSV translation--is it better to wait and get a better translation or just use this one?
You can use that if you want. Personally, I agree with the late Fr Thomas Hopko that the NRSV is just horrible and think you'd be better off with another translation (I prefer the "old" RSV, but I also use the NASB), but I'm not sure it's so horrible you have to avoid reading a NRSV Bible entirely until you get a better translation. Just be aware that it can be awful when it's bad.
I will second this. I had bought an NRSV when I was in the inquiry stage because it was cheap and had the deuterocannon. I quit reading it soon on as the translation was just so egregiously horrid.
I will also say that I see nothing wrong with humming or singing bits of Liturgy - in fact, I would say it's a good thing that shows it is sinking in.
As for the rest of the OP:
Bible studies: I'd personally sit them out. At the best they are just going to be namby pamby fluff and filler, bits of feel good philosophy and spiritual baby food. At the worst they're going to be teaching things outright hostile to Orthodox doctrine.
Orthodox "bits": I would caution on sharing too much with those who are opposed to Orthodoxy. There have been a few times I've answered what seemed an initially innocent question only to have the questioner end up screaming profanities toward the end. It didn't hurt me, any, but I think it wrong to provide others with an excuse to blaspheme the Holy Spirit.
Joining their services: I think this requires a bit of parsing. By "joining" do you mean joining with
them for services? I think doing this occasionally is fine, especially for special events like weddings and funerals. If you seriously believe what the Orthodox do about our sacraments, then don't join in on communion.
If by "joining" you mean joining in their prayer, adding an "Amen" at the end, what have you, then no, I don't think that's so good. That said, I've been known to jump in on a rendition of "Amazing Grace" from time to time.