What do school say? What are her friends like with these things?
Re the toys, a lot of toys are given to children too young. Eg sylvanian families are given to very young children but if you think about the detail and small parts, they are actually much better suited to older children. It's the same with lots of other toys.
When I was in college, a lot of students watched telly tubbies and the like. I think it was mindless nonsense that relaxed them during stressful times.
Temperature tantrums sound very teenager-y! 🤣
A lot of children are too advanced for their age, or at least act and look that way. One of my daughter's friends had a proper boyfriend at 12. My daughter didn't even start noticing boys in that way until she was almost 15.
If she needs a bra, why not start with a crop top or sports bra? These are a bit more vest like than a proper bra and might help her get used to the idea.
Does she have any independence eg does she walk to school by herself? If not, could she start walking the last 5mins and gradually build it up? If she already does, why not push it a bit and arrange to meet her for afternoon cake, a little bit further away (but somewhere she knows really well). Don't be forceful but do keep coming back to the idea if she initially says no. Or catching a bus with you seeing her off and someone else meeting her at the other side.
My daughter still dislikes being at home by herself so I don't think she's ever been alone for more than 30mins. Not great but we've never needed to.