You're probably reading too much into it. She sounds like a fairly typical teen experimenting with different styles in an effort to "find herself" and what have you.

As for the text conversation with her friend, saying it doesn't make it true, and she thought she was having a private conversation (does she know you check the texts periodically? If she does, fine, if she doesn't, that's not cool. She may have been trying to impress her friend or sound cool, or make her friend feel better about her bad situation, or any other number of justifications that go through a 13yr old's head.

I do agree that she could have less of an attitude toward you and her sister, but that's also pretty normal. As for the haircut, nstead of outright saying no to what is ultimately a pretty harmless thing, I probably would have said something like "You didn't like it the last two times you tried it. Really think about it for a couple of weeks and then if you still want to do it, you can, but you don't get to complain about it later."

If she's otherwise a normal, well-behaved, doing well in school kid. I would try not to read too much into it. If you're really concerned, you could talk to her about it, but I wouldn't punish her for the texts