Why can't I get the physical keyboard to work?

Which model is your Mac mini? "Amazon keyboard" does not tell us much. We would need to know the make & model. AFAIK, Amazon does not make keyboards.

Also, are all of these keyboards wireless or wired versions? If wireless, and Bluetooth does not appear to be working on your Mac, none of them will be able to connect.

No idea as you haven't provided us with any details ... like what is the make & model the keyboard is and what you are trying to connect it to.