Only if you want to go, and if you know that she is probably the one. If your relation is poor, then you should just stay home and text her. It really depends on your relationship. I think you should defiantly go, but I also think you should let your relationship do the talking. I hope this helps.:)
Depends how serious you are about her and the relationship. If you love her and want to spend the rest of your life with her, then yes go with her. If you love her but aren't sure if you want to spend the rest of your life with her then probably not.
Ask her, talk with her see what she wants if you don't know the answer. You didn't say anything about statues of your relationship so it can be one way or other depend on how serious the relationship is.