First, if you are under 18, you shouldn't post your age. It's against the rules, so you should edit that out. You can just say you're a minor.
1. There's two options. But one you have to be 18. So for you, the process would be going to a gender therapist (no time requirement) and making sure your parents are on board. The therapist after a few sessions or maybe longer depending on the therapist and you, can write you a letter for T to bring to an endocrinologist who works with trans patients. [This does not HAVE to be a gender therapist, I have had friends get letters from their normal therapists. The therapist had to learn how to write the letter, but they are still qualified to do it.] With parental permission, you can start T. Most doctors require you to be 16, however, you may be able to get on hormone blockers or find a doctor who prescribes younger. I've heard of guys as young as 14 getting on T. Depending on who you can find the requirements can range from 14 to 18. The other option, where you have to be 18, is to go through informed consent. Some doctors make you sign papers saying you understand the effects of hormones, the doctor talks to you about that, then you get to start. You basically sign a document saying that you know full well that these changes will or will not occur on hormones, so you can't get mad at the doctor and try to sue them or anything. No gender therapist needed here, you just go straight to the hormones.
2. After reading your whole post I'm a little confused- does everyone at school use Max? Are you stealth right now, or do most people use female name/pronouns? Well I guess Max is a gender neutral name. Could you explain your situation further?
3. If it is a name you love, you should go for it. If your family has issues with it, perhaps they can use Maxwell or whatever longer version you like, or they could use whatever you'd like your middle name to be? It's not unusual for family to use one name while non-family or friends use another. Some families prefer the full or formal versions of names, or they use first names when people prefer their middle, so it wouldn't be unusual if others heard them using a different name.
If you have other questions, feel free to ask! We are here to help 🙂