Weird converstation

Yes, I think your thoughts are quite normal in this instance. You sound like a pretty good guy, and I think your feelings are more than understandable. You have a right to your feelings, and although you do sound quite well adjusted you also have the right to not respond to her or to distance yourself from her. It's quite possible that you'll find someone much better than her!

From what you're describing she needs a counselor, therapist or maybe even a priest or minister more than she needs to use you as a platonic male friend to torment with her issues. She might not be mentally ill, but could most likely use some guidance in regards to empathy. I had a really good Christian/Catholic therapist for a number of years who taught me that self-esteem is more about being esteemable than simply fishing for compliments. Don't respond to her comments when she says she's ugly, worthless, etc, because she's fishing for compliments. She might not be actively aware of it, but she's still fishing. You've got better things to do with your time than stroke her ego via reassurance.

I am curious as to who instigated the chat friendship now though.