I have an unlocked T-Mobile iPhone 5s that I put a Freedom Pop sim in as a "guest phone" for my visiting Non-US Friends and Family.

It seems to work just fine. It is strange that its not a real phone number, only a VOIP style app - but it still works with iMessage and WhatsApp, and they can make and receive calls in a pinch.

FreedomPop sells AT&T SIMs. The phones they sell are for Sprint. I have accounts on both. I use the free AT&T SIM in my car and get 1GB free/month, which is more than sufficient for my Google Maps/Earth and directions usage.

It's complicated. In general, no, due to different base technologies (GSM vs CDMA), and the US carriers' unlock policies (the carriers can sometimes lock your phone to their network). In specific, maybe, because some phones (mostly new iPhones and Nexus/Pixel devices) can be used on all US networks, and the CDMA carriers have started to use SIM cards like the GSM carriers.

Not an easily answerable question, and no one is giving you the real answer:

look at the specific bands that your phone supports. there is no other way of knowing. a good amount of phones are CDMA and GSM. if your phone is carrier locked, you will also need to find a way of undoing that.

Freedom pop has a contract with at&t as well, you need one of their at&t sims tho.

I have one in a spare Verizon note 4 - it gets h+ networking rather than 4g, but its useable.

No, Sprint is CDMA, T-Mo/AT&T are GSM.