I have limited experience here from my DD1
On the lesbian side of of the issues, she may be experimenting (in her head rather than in actuality) with her feelings rather than being sure about it, BUT there is the equal possibility that she is indeed gay, and this being the case, it can be a really awful time emotionally.
My eldest daughter is 20 and lesbian. She was pretty sure from about 14, dead certain from about 16 but only actually came out in February this year. I had NO idea. I have a close and loving relationship with her, but she has always been quite a private person emotionally, and when she told me I was very upset.. not about her being gay..couldn't give two hoots about that, but that she had struggled with it for so long, alone..she had told no one except her last boyfriend, who was perfect in every way except he was male!
She became anorexic in her first year at Uni ..partly uni stress and homesickness, and partly from the sheer emotional overload of trying to be 'normal' (her words) ..hence the boyfriend . Her recovery (ongoing but good) from anorexia started when she came out of the closet.. the relief went far deeper than even she knew. Like your daughter, she is very bright, and somewhat introspective.
I wish, wish wish my daughter could have confided in us when she was 14, 15, when we would have supported her just as we do now.. we are very proud of her and the courage it took her to come out.
I think if there is any way you can subtly let her know that you think gay women are fantastic and that you would be as delighted with a gay daughter as a straight one..(or as we did.. we couldn't care LESS about our children's sexuality as long as they seek loving, mutually respectful relationships) you can maybe help plant the seeds that it's OK to be who she is. My daughter knew this, but still somehow thought we would be disappointed in her and more, she didn't want to be different. But now she has accepted that she IS, she is happier.
Would it help to write her a letter?.. you could explain how you came across the chat site accidentally and that you love her to bits and want her to be happy?
The self harm is worrying..but I wouldn't push the panic button on it because confronting her might make her careful to hide it. My other daughter self harmed briefly during an unhappy period (she was 14 too) and I was very upset when I found out, but I asked her to tell me when she felt like doing it so we could find another way to release her feelings together.. and it did stop.
Sorry this is long.. not sure what I'm trying to say except she needs to know somehow, and in a non confrontational way, that you are aware, that being gay..if she is.. is ok, and that you will support her in any way to help her stop self harming, if she is.