The OP does state that there are multiple instances of bullying - hiding clothes, throwing a lunchbox across the floor, one boy bit the victim, they chased the boy, either these all happened in one frenzied attack (unlikely), or it's a sustained, low-level bullying which isolates the poor child in question.
Of course the OP has the right to speak to the school, but she should be in support of their decision rather than being upset that she feels her child is still being "punished", when in actual fact all that is happening is that the gang of boys who are bullying have been separated so they can no longer gang up on other children.
I haven't spoken about the 8 year old badly, so that's irrelevant.
Of course children mess up sometimes and I have never stated otherwise, however if a child decides to bully another child, there must be consequences. OP's son may have "messed up" and now he has consequences which prevent him from messing up again. It wasn't an accident that OP's son did any of these things and 8 year olds are old enough to understand that these actions would have upset the boy. These actions were done to upset the boy they were bullying. OP's son is now being taught that if he and his friends purposely upset people in school, a place where ALL should feel safe, he will not be allowed to play with the group he has been bullying people about.
If OP wants to work with the school to ensure that her child does not go down the path of being the "school bully" (baring in mind a lot of these start when they are very young) then she should have every right to do so, I agree.
With the apology though, I think OP's son should only be able to apologise to the child if the child wants to. I received many disingenuous apologies from my bullies, forced by teachers, in school. They were excruciating as I knew they meant nothing and it tended to just ramp up the bully's behaviour afterwards so they didn't feel they'd "lost".
The point I'm trying to make is that yes, children can and do make mistakes, however this isn't a mistake like knocking over a glass of water, or forgetting to shut the fridge. This "mistake" needs to be nipped in the bud because no matter how sorry for himself OP's child is feeling, there's another 8 year old out there who will have been dreading attending school because of the actions of OP's son and his friends and that is simply unacceptable. The school are right to put into place this plan to stop these boys bullying and OP should work with the school to support this rather than take up the defensive, as she so clearly has been in her previous posts.