Gunpowder has it's own oxidizer, I don't see why not.
They would, though the difference of pressure inside and outside the barrel could be a concern.
Gas also expands faster in space, it's not limited like it is in atmosphere.
The idea was that recoil from conventional weapons would be too strong in space, so they decided to try using tiny rockets as bullets. I imagine they worked pretty well in micro gravity, but were ultimately too expensive and unneeded
Russians tested a 23mm gun on one of their spacecraft. The craft was abandoned and fired remotely due to the shaking that would arise.
From what I'm reading, Gyrojets were highly susceptible to manufacturing flaws.
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