With Windows as I know it,...when you login YOU are the Root user and thus administrator....
No. Each machine must have at least one account with admin rights. As IT/admin, you log on and can create user accounts with various levels of authority. So create a generic user profile or one per student, and only give them that user name and password. That was the way it was always done on mainframe systems and it worked just fine.
By default, yes you can. But a competent sysadmin in a school especially, should set kids up as user-level with NO s/w install privvys.