Restrictions on Moderator

Depends on the detail of your question.

All the following is only achievable using the backend.

Out of the bix, if a moderator/admin creates a forum, then an admin can limit access to that forum to one or more users, which can of course be just the moderator or a user.

You could use a management plugin such as Advanced Access Manager to allow moderator access to the private groups settings ,and then a moderator could create and administer the forums and access to them.