Is there a way to limit the number of students to 50 per date and location

Yes, please check this guide on how to set a limit submission: https://www.jotform.com/help/137-How-to-Limit-Submissions-in-a-Form

Also, check here this guide: https://www.jotform.com/help/64-How-to-Set-Unique-Submissions-on-a-Form, in order to set a limit per location.

Let us know if you need more help, we will be glad to assist you.