That sounds somewhat like me, at least the bit about varying obsessions which come and go.
When I was 8, I discovered that I wasn't doing so badly at school. So getting only As became my obsession for two years. Then I wanted to be a cartoonist with 10 and drew comics on hundreds of pages. Eventually, I dropped that too. With 15, I got into programming and Computer Science. That kind of went on until now, although I'm not sure if I'll continue with it.

I don't know if this constitutes a mental illness. In my case, just the fact that I have a lot of ever changing interest is kind of annoying to me, because I'd like more continuity in my life. My problem is more connected to the fact that I reach a point with every interest where I get more and more anxious about not being good enough, which plunges me into severe depression because I centre my whole life around these interests.

Is your daughter happy with her way of life? Of course it's an issue that she has a hard time supporting herself, but does she see those things as an issue herself?