Yes it is possible. Just run the tank with a clean up crew for a few months though while you get use to maintaining the salinity and other parameters of the tank.
Yes, it is possible. I have a 10 gallon Nano right now. To keep water quality up, I would use live rock and do partial water changes every other day. (small 5%)
I would use a small HOB external filter with a little activated carbon. For a clean-up crew I would get a few Blue legged hermits, some Astrea snails, and maybe a small serpent star.