OP, saw your update and, as another poster suggested, it is 100% appropriate that you report the self harm and suicidal ideation mentions to the designated safeguarding lead at the school.
Regarding one of the girls being bi-sexual, to me personally I would try not to speak of this in the same terms as the gender-identity stuff.
Sexuality is something it is totally reasonable, in my opinion, for pre-teens and early teens to start considering. I certainly knew I fancied blokes by the time I was 10! Nothing inappropriate happened to me - I just had crushes and romantic fantasies about them - but it WAS an indicative precursor to my fancying blokes in the future, and I was aware of it. Actually turns out I am bisexual and it took me till late teens to accept that fact, for whatever reason.....
But what I am trying to say is, please don't make your daughter feel that being straight, gay or bi is on a par with being non-binary. I know they all get lumped in together with the term LGBTQ+, but I have literally no idea why.
On the other hand, if this child is genuinely "pressuring other girls to be bi" that sounds potentially like a form of child on child sexual abuse (is she pressing them to kiss her or is touching involved for example? Etc?) so again potentially needs reporting.
Sorry, it's a whole awful mess of stuff you are dealing with here.
And I massively don't want to make light of it because it could actually be that some of these issues are really serious here, as I have said above.
But ALSO please be aware that (this sounds awful, and PLEASE understand the spirit in which I say it) talk of self harm and suicide is fashionable and trendy among certain sub-sets of kids - the closest approximation I can give is it's like a "goth" thing a bit, tho they aren't quite like goths as we might know them.
So it may well not be anything kids in your daughter's circle are actually contemplating or doing. Hopefully just a pose. A harmful and concerning one, I agree.
Good luck OP. You sound like a loving and concerned mom, and she is lucky to have you on her side.