My son has similar issues and is only on kindergarten. I spend a ton of time at home going over homework and trying to prep him for the next week(I ask to get the main points of the next weeks lessons sent home each Friday). That tends to give him a leg up and therefore more confidence in the classroom.
As for out of seat behavior, he doesn’t have too much of that at school according to the teacher’s feedback but he has tons at home. We initiated a seatbelt at the table. First we described how this would be carried out, showed him what we were using and gave a demonstration. Then we explained it as an aid to help him remember that he is supposed to be seated and told him we would begin using it in 3 days. The belt is a reminder not a punishment and he agreed that this would be something he would be happy to have since it is no fun getting constant nagging to stay in his seat. So far it has worked great. He still fidgets a lot but stays in his seat. He still has bad days so there have been times where he just lets himself out of the belt but for the most part, he really appreciates it as an aid.