I'm in the same boat as you. Just waiting on LOE. I got an interview invite to NOVA, and that's the only school I've read on here that does that. I could be wrong, but I wouldn't bank on anything else.
I got interview from NOVA without the liberal art LOE. I also heard that Columbia will give out interviews even if you don't have the third science LOE (correct me if I'm wrong) 🙂
Depends on the school, some will and but most won't, especially if you're missing entire committee letter. It is still super early in the cycle, I wouldn't worry too much.