Under the non-commercial license, you can duplicate the rig file as many times as you wish, and transfer it to multiple devices owned by you. But you can't share it with anyone else. Under the commercial license, we define the business entity (eg. studio, not school) owns the rig file. For instance, the rig file can be passed around with multiple artists inside the studio. But certainly, the studio can't share the rig file outside the studio. For more details, please refer to Terms of Use.
This is a special exception, and the answer is yes. But this is only under the case when the rig file is owned by the teachers, not the school. We will assume that the teachers only make money by getting paid regularly from the school. The teachers shouldn't share the rig file with any students under any circumstances. The rig file can only be used to help improve presentation purpose.
The commercial license is mainly designed for studios or individuals who want to use the rig to make money. When a studio owns a character rig, the studio can pass the rig to multiple artists on multiple shows. But artists are not allowed to bring these character rigs back home. Please be aware that school can't purchase the commercial license. For more details, please refer to Terms of Use.