The sentence is gramatically correct, but it does not sound very natural. First of all, quite often in japanese oral, subject is obmitted. Second, it is rare for japanese to say "anata'. Instead, they use family name plus "san".

Yes, it is. Addition: I think "watashitachi wa anata ga daisuki desu" is more natural, in this case. ( suki = like , daisuki = like * very much )

Yes, that's right. If I were you, I'd use her name+san(suffix) instead of "anata," but that's not a big matter.