Is it normal for a 24 yr old woman...

Maybe she just wants to try and forget the failed relationship happened and try to recaputre the time she wasted. It's what I would do.

For a woman to want a younger man, normal. But if I were her, she should go for someone whose at least 18, so she dont break the law.

I don't see the problem. There are just lots of assumptions.

its funny because I hang out with a 24 year old woman as well!

As long as they are good friends, and don't brake the law. I don't see anything wrong with it, in my point of view.

If she has "feelings" for them she doesn't act upon it, but she gets mad if they don't want to hang out with her.

You mean hanging out as friends, right? Age doesn't really matter..anybody can be friends if they share common interests.

I have a friend who likes younger dudes. She is 26, and she likes 18yr olds, but recognizes it's not really appropriate.

It's been my experience that younger dudes think I am "really cool" and will agree with and do anything I want. I eventually get bored and frustrated with it and end up treating them badly, till it ends.

are you feeling insecure?

It depends... is 17 the age of consent where you live?