I was very confused as to why they could be fooled by Amy not seeing them...or something?

I think that part was just stupid really, and seemed to go against what we knew about the Angels already. I'd really recommend watching Blink from the third series, which is the first time they show up - it's basically a stand-alone so you don't need to know anything, and it's the best episode of New Who.

I don't ship Doctor/Amy either, and I was totally embarrassed by her throwing herself at him. I see it as more of a big brother/little sister bond.