ok so I can answer this from personal experience :) So yes most of the time it's because you realized the person you randomly looked at was good looking but sometimes..you might think they look like someone you know (which happened to me before)
I wouldn't do a double-take on a guy if I wasn't attracted. So, she probably was
It means that she either found you attractive or strangely unattractive. Honestly no way to know. I would say in general it is because she finds you good looking, with the exception happening occasionally.