Applying to sixth form as a trans student?

I'm sure if you ask the school and find out beforehand. It's like, basically illegal for a school to be transphobic and not respect your wishes. In my school I've met 2 trans students. One of them ( Eva -> Evan ) after having a conversation with the teachers got the teachers to call them by their preferred name (almost like a nickname) despite having the deadname on the register. The 2nd trans student got them to completely change their name.
You just have to ask. Although, downside is, if you're going to be signing documents (e.g. exam wise) you're going to have to use your deadname if you don't want your parents to know.
Yes, it is more than likely possible in 6th form.
If you use your new name on legal documents it might cause some issues (e.g. parents finding out, identity issues [ unless you can legally change your name ]), just ask your school.
You can ask for it to be confidential, otherwise yeah.
It depends on how comfortable you are in your own skin. If your parents are stopping you from being free, yeah, you might have to wait a bit. If you're okay with them possibly not accepting you, you're free.
Talk to the school.
Here's some helpful stuff I got off quora that you might find useful to you, since I myself am not trans:
"For dealing with university administration, you probably need to use your legal name for legal forms, but ask for guidance.
For your teachers/professors, I recommend doing what my first trans student did: contact them ahead of time, explain your preferred name and pronouns, and introduce yourself privately before class. That helped me a lot.
I’m sure some people out there will intentionally call you by the wrong name or use the wrong pronouns, but they’re probably far in the minority. However, it can be difficult to manage lots of student information, so help your professors and, if they misgender you or call you by a non-preferred name, start by assuming an error on their part, rather than discrimination."
"For legal and safety purposes, since I was always anxious about this sort of thing myself, I would sign everything important that might need filing with your legal name, until you're able to get it changed legally assuming you haven't already. And, who you tell is up to you. If it would make you more comfortable at school to be addressed differently than you are, absolutely tell whichever teachers and students you feel like telling. I'm not sure what the social climate is like wherever you go to school but, in most of the US, schools have known LGBTQ ally clubs and some teachers will likely have maybe a sign or two indicating their classroom is a safe zone. Some teachers might be a bit weird about this kind of thing admittedly, so it might be best to start slow and tell teachers you trust most first and see how they respond. In fact, it might be a good idea for you to go and discuss this with a teacher connected to the ally club in some way to see if they have more educated advice and if they might be able to calm some anxieties about telling certain teachers. After this, you could absolutely sign essays and assignments with your preferred name, so long as the teacher is one of the ones who know and won't throw it out by mistake. Unfortunately some students and in some parts of the country even occasionally teachers might be a bit rude. But you might be able to tell who might respond poorly and, acting rudely toward you for something like this directly is absolutely unacceptable. In those situations I'd speak with some higher faculty or one of the ally teachers I mentioned before."