If I delete form responses, does that open up space in my 100 total responses?

If I delete old submissions, can I continue to accept new ones as long as I never have more than 100 saved to the system at one time?

What happens to submissions that go over the 100 mark?

No, deleting submissions will only affect the available space to store information (uploaded files), but will not affect the submissions counter. The submissions counter gets reset only once at the beginning of each month. 

If you reach the monthly limit (100 in case of free accounts) the account will get disabled until the beginning of the next month or until you upgrade.

You can see here more details on the monthly limits of each plan:

https://www.jotform.com/pricing 

Let us know if we can assist you further.