Awww, I really feel for your son after reading that. I remember starting secondary school and worrying who to sit next to in the lessons because I worried the other kids wouldn't like me enough to sit next to them. The first few I sat by myself and did feel very isolated, but I was lucky enough to make some friends after a day or so. Even now as an adult (and I am a teacher) I hate going to courses alone as, again, I don't know where to sit, and particularly hate the break times when I have to force myself to talk to people, which I do and then sometimes enjoy meeting new people, but for a child that's a very difficult thing to do. So I really feel for him that he is spending his break times just walking to the next classroom and waiting for the lesson to start! That's no way to spend your school life, poor kid. His form tutor sounds like a horrible cow as well, which is probably why he isn't making friends as she's obviously not very good at spotting kids that need a bit of help doing so and then giving them the help they need. And her blaming him for not joining more clubs is stupid. It isn't friends in clubs he needs, it's friends in his classes so he has people to hang around with at break times. I'm sure if he was part of a group, the name calling from (I'm hoping) a minority would stop. Or even if it didn't, I'm sure it wouldn't feel so bad if he had friends to be with.
I sympathise about the behaviours that get him down. I was fairly naive when I started secondary and I think some other kids guesed this as I got a few comments such as 'do you know what sex is? I bet you don't. My mate wants to have sex with you' etc etc. But I could brush things off as I had friends. I was never seriously bullied I think because I had an older brother who was very much in the 'popular' group in his year, which was a lot nicer than mine, and I knew, and I'm sure everyone else knew, that he (and his friends) would stand up for me if needed.
Your son must have been at the school for a term and a half now, which is a long time to feel miserable, poor thing. Ok, as to practical advice, it's difficult as he has a rubbish form tutor. I think your next step would have to be his head of year. Generally a sympathetic teacher is assigned head of Year 7, so you might get more joy there and he/she might also have words with the form tutor and make her do something.
If the drums in the music room is his only sanctuary, then find out what the rules are so that your son can stand his ground. I'm sure those older kids just made something up to get him out of the way, but I can imagine that if someone had said to me I was banned, no matter who said it, at that age I would be too scared to go back. So clear that misunderstanding up so that he knows he has teachers blessings and is definitely allowed in. Also, there might be other kids in the year who play drums, but don't know they can use them at lunch times. Perhaps the Head of Year could find out and try to suggest it to a couple of them, so your son can get to know them at lunch times.
Probably he is only finding the work too hard because he is so stressed about everything. If he felt happier then he would probably relax and find it all a bit easier, as if he got Level 4s he should be doing quite well. Having said that though, if there is/are one or two subjects that he is finding really difficult then it might be worth getting a tutor for a few weeks to help to build up his confidence.
Where did the rest of the kids from his primary school go if only a couple of them have moved up with him? Is there no option of him going to their school?
Are there any children who he feels he might like to be friends with? Does he know what they do at break times? I'm sure he will feel very apprehensive about doing it, but he might need to force himself to just go up to them and join in. Suggest things for him to say, such as, 'Have you done the homework for the next lesson? Did you find it hard? I did.' He might find it easier to talk to people if he has a 'script' to follow to begin with.
If there is really noone who he thinks he could be friends with, which is possible knowing the behaviour at some schools, though usually there is a 'nice' group, then you may have to consider another school. If it has a diferent attitude, no tolerance for bullying etc, then it could be a completely different atmosphere for your son and he could love it. I would try and encourage him to open up a bit more to the other kids for the rest of this term, speak to the Head of Year etc, then if nothing has changed by Christmas, look into moving him, as a term is a long time to have hated somewhere and it's best to get settled somewhere new in the early years of secondary if possible.
Also, don't rule out home educating him. There is quite a lot of support, and you could maybe have a tutor for a couple of subjects once or twice a week if you feel he needs specialist teaching. There are a lot of text books, workbooks, the Internet, etc to use as well.