The very first comment:
Unless you believe in magic, the human brain proves that human level general intelligence is possible in our physical universe, running on a system based on the laws of said physical universe. Given that, there's no particular reason to think that "what the brain does" OR a reasonably close approximation, can't be done on another "system based on the laws of our physical universe."
Yes, and they are not required to run in a primary because those are run by each party (being independent means you don't have a party to begin with)
There's no limit (AFAIK) to the number of candidates on the ballot, but there is a deadline to file and that deadline has passed. Cuomo had preemptively filed as an independent candidate in case he didn't win the primary (I think Mamdani did this too), but had not publicly stated whether he would use it until now.