I'm not much older than you, but sometimes a few years can make all the difference. I am not male to female I am androgyne, but I would like to try to support as much as I can.
The first thing that I want to say is that all trans women are real women. All trans men are real men. I was not offended by your questions at all, because especially at such an age it's so freaking easy to doubt yourself. I do it all the time and it gets hard. Sometimes I feel like it's fake and that I should try to be "normal". But you are a woman. You are made to be a woman, and you're not a "man trapped in a woman's body" you're a woman, in a woman's body. Women have all kinds of bodies. There are women who are bigger and there are women who are smaller and sometimes they feel uncomfortable about their bodies, and when they do they work to change it.
Coming out is a very scary process. But remember, you don't have to come out. It's not manditory for you to come out, it could make it easier but if you decide that coming out isn't for you, you will simply just take a different path.
From what you did say about your parents, I think that they will love you unconditionally. We fear what we don't understand, so maybe they just don't understand transgender folk. But you are their daughter and having that close relationship with them can help them to understand. It will be hard at first for them to comprehend what you will be saying, and they may even lash out, at first but sometimes you just have to be prepared for it. I think that after a few months of coming out they will be more used to the idea of who you are. When you first come out parents are typically very shocked and feeling a lot of emotions, so be prepared for questions, accusations, and the whole deal. They may even say something that hurts your feelings or invalidates you.
This does not mean they don't accept you
they are just trying to deal with the shock of it.
Be prepared to tell them calmly, "This statement hurt my feelings because it makes me feel like ___"
Be prepared to answer questions that seem unnecessary, so you'll want a better understanding of yourself than anyone.
They might ask what you want to do now that you've come out, write down or have ready your end goal whether you want bottom or top surgery or hormones or anything else, including what your pronouns are and that you are their daughter.
They can help you from there.
If all doesn't go as planned (I think it would, but I don't know for certain)
indulge yourself in feminine things to try to relieve yourself of the dysforia, come out to peers at school so you can have a space where you are accepted as you, watch tutorials online on how to tuck and how to make yourself how you envision but with supplies at home. Please keep looking forward. As my signature says, they can take away all of your tools to help people see who you are But they can never take who you are
You are a woman. You're not just a man dressing up.
It's hard. I definitely know that. But I personally believe in you and I want to help you and support you with every part of my heart. Any time you need help, please come to me, or anyone here. We want the best for you. I want the best for you.
Sincerely,
Patricia.