I didn't know where to post this so don't moan if it's in the wrong place!
My question is:
Can moderators/super moderators ban users or can only admins?
No, they can't, unless you give them restricted access to the Admin Control Panel (using User Groups settings and Admin Permissions).
And this is in the wrong place, so I'll move it to General Support with a 3 day redirect for you.
By default, no like Justin said, but with a third party plugin,
Forum Warning System, they can without the need of ACP access.