My son has some similar issues, although his school is actually pretty fun and they do have recess every day. I hope you are able to find some ideas for how to get recess to return - I've heard of parent groups (in other states) going to school boards and challenging to get recess back, but tread cautiously as a new parent to your school district - you may be surprised to find out that lots of parents seem to think first graders should have longer days, more homework, etc.
It sounds like your son is in first grade? It's kind of a shock because it is a hard change from preschool and kindergarten. Anyway, if he is writing, you could talk to his teacher about having him start a journal where he can write down the answers he knew but didn't call out, and the teacher could discuss/praise him at some more convenient time when the other children won't be disturbed. Another idea is to have him keep track (in a journal or whatever) of every time he knows the answer but doesn't call out, by just making a tally, so that he can see his own improvement.
It does suck, I agree. I was with my son at a children's program at a museum this weekend and they were asking the kids to answer questions, and he knew something none of the other kids knew, and gave the answer, and I was terribly impressed with him and proud, but then he looked at me like he was afraid I would be angry (because he's always in trouble for calling out answers!) Unfortunately, it's not fair to the other kids if your kid is ALWAYS the one with the answer. They have to learn to wait their turn.
Another thought is to talk to whoever - special ed or gifted person - about "twice differentiated" kids, who are both gifted and have a learning and/or behavior disorder. You may be able to get accommodations, but every district is totally different, so I don't know what might be available where you are.
I don't have an answer about the boring work, but my son struggles with the same thing. It's not that he's all that brilliant (although he is bright) but that he has very few inner resources to deal with tedium. And tons of energy to take on projects at home, so he keeps us busy (right now we're learning about how to do your own animation because that's what he wants to learn about.) Good luck!