Sometimes, the teacher wants to know what each individual pupil has grasped from the lesson or knows already on a topic- so if one student is talking, even about the work, this isn't helping the teacher or their classmates.
Sometimes, talking about the activity is ok.
Sometimes, off topic talking will distract others, and it means the pupil isn't working to the best of their ability. In many lessons, a few minutes is lost at every "transition" due to pupils talking. If you say 5 minutes is lost per lesson, then that's maybe 30 minutes per day, or two and a half hours a week of lesson time which students are missing out on.
Shouting out is never ok- it doesn't matter if it's correct or relevant. Teachers often want to give every pupil a chance to answer, not to allow your child to dominate the lesson. It can be intimidating for shy pupils and put them off answering.
When you talk about being hyper, this sounds like low level disruption and isn't fair on others.
It doesn't matter if all their work is being done if they are negatively impacting the class around them.
At some point, your child will have to learn to sit quietly and concentrate- either at university or in the world of work. Why not start now?