Let's look at those things you have mentioned:
- only wears underwear (bra and knickers when going out) but will happily wear briefs when indoors (not bra though).
- has never even tried make-up (I know this doesn't mean anything but with everything else).
- has an obsession with getting short hair with a fringe (like old Justin Bieber hair) and often takes photos with her hair looking like that (tying back up and making a fringe) - she does this a lot.
- talks about how she would love to be able to just take her top off when it's hot/swimming, etc.
That, taken together, leads me to this, totally reliable diagnosis on a child I have never seen:
Congratulations, you have a feminist!
She doesn't want to perform femininity and resents the sexism and male gaze that force her to wear a top. All typical traits of feminists!
You say there are more. What more is there?
Those things you mentioned sound very much like she's a feminist, whose identity you should support by buying her books by Germaine Greer.
Nothing so far points to her being transgender.
And you really, really, really shouldn't put that transgender idea in her head by asking leading questions. You don't want her to start hormones and surgery, do you?