Can I allow athletes to register for one division and/or various divisions?

Yes, the software allows any fighter to register as many times as you decide per class. In the bottom of each class setting you will find the setting for multiple registrations.

To change the number of times an athlete can register for an entry, go to the "Settings & pricing" on the entry and scroll to the bottom.

You can also copy a fighter from one class to another with the copy function.