One normally thinks of photons as being associated with light, not with microwaves, but all electromagnetic radiation consists of photons, from radio waves through gamma rays.
Old joke among physicists: Photons have mass? I didn't know they were Catholic.
The "paradox" is that they carry momentum without mass, a privilege of masslessness, paradoxically.
Nope. Nothing is being ejected directionally. That's why there is a big question about this. If it was simply shooting microwaves out the back as thrust, that would be different. The thing that is weird about this is that as far as we can tell, nothing at all is leaving the chamber.
If the observed thrust turns out not to be a measurement error, this is huge. It will revolutionize what we can do in space.