[mothered]

facebook banned people for up to 7 days for posts that had nothing bad with them

Given Facebook banned people for 7 days, they'd have probable cause to do It. Meaning something (content or otherwise) must have violated their terms to some degree.

he also participated in insulting everyone once again. talking badly about the group and the people there.

Is this against Facebook's TOS? Clearly I believe It Is:

You will not bully, Intimidate, or harass any user.

Source: https://www.facebook.com/terms

but reporting is clearly not an option here

Judging by what's documented above, I think reporting Is well and truly an option.

Oh and also, is there any way of facebooking unbanning an account?

It depends "why" the account was banned. That's something you need to address with Facebook.