1. The house in which I live is very large.
2. The house which I live is very large.
#1 is supposed to be correct. Is #2 also acceptable?
No. It needs in after live.
I'd also say "that I live in" and not "which I live in" 100% of the time.
I'm not a teacher, but I write for a living. Please don't ask me about 2nd conditionals, but I'm a safe bet for what reads well in (American) English.
I think I would mostly use The house I live in is very large.
I live in a very large house.
Show-off! I live in a small flat.