General knowledge helps. You don't need to know much of the war history, it's more about character personalities and interactions they had. I would know that at the end of the actual movie that happened after Gundam Wing they basically all swore to never kill again. Most other stuff you can gleam from a wiki if you need to.

Good notice. I drop that hint later in 0050 Rider (Part 3).

I have been debating on the answer to this one, especially since it's not just up to the women in each dimension and the gods aren't created in the same physical way as humans too. I am going to save answering this until I get a little further ahead because if I answer it completely, it will spoil plot twists in each dimensional story. For now, I would say . . . no for sure for the manga version. I wouldn't expect full on romantic gestures with a bunch of characters though, and I am not getting into physical descriptions in this fanfiction.