Questions and concerns about my dove.

So I have a ring neck dove named donna. She randomly flew up to me while i was walking my dogs and i've had her ever since. I've never had a bird before. I looked up some information and I have a decently large cage for one dove. Some questions i have is that:
1) My bird seems a little too attached to me, is this a bad thing or should i become more distant?
2) I don't have any toys for her to play with. Where could I get toys for her?
3) At times she would go on my curtains and coo while twitching her wings for minutes at a time, why do they do this?

Thanks so much! <3