In space, impacted objects tend to move in the direction of impact. Near-body gravity has minimal effect on the motion of objects when they are perturbed by larger outside forces.
In Outland, during the fight scene outside the space station, an enemy apparently falls "down" to his death under the apparent influence of gravity, just like on Earth.
Dude, they're not "in space". They're on Io, a moon of Jupiter. The surface gravity is about 18% of Earth's - that's more gravity than there is on our own moon. It's true that the film has some issues with how it shows gravity - people outside are shown running just as they would on Earth, rather than the kind of loping bounce you see in the Apollo footage. But things would fall just fine on Io, if slowly. They actually get this just right in the climactic fight, when guys are shown falling pretty long distances without major damage.
But if you fall long enough on Io, you'd still build up a fatal speed. For instance, if you fell 100 feet you'd hit the ground at only 7 miles an hour, which is easily survivable - and Connery does just that, dropping down onto the bad guy from about 100 feet or so.
But fall 1,000 feet and you hit at 74 miles an hour, which is easily enough to kill you - and that's just what happened to the bad guy at the end. (Though he'd be dead anyway since Sean ripped his air hose out.)
Also- do shotguns function in space without oxygen?
Yes. There's Oxygen built into the propellant used in bullets. Guns would fire just fine in space as far as that's concerned. The only issue you might have is that the surface temperature on Io averages -261 F, which would probably freeze the oil and cause the gun to sieze up. But we could probably make oil suitable for that temp now, if we really needed to. Certainly it's no big stretch to assume gun makers of the future would have a suitable oil.
Shotguns would even be a decent choice for a space gun since they are less likely to penetrate walls than a solid slug.
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I think they were on the moon Io which is 1/6th that on Earth. Like on our moon, really.
I think shotguns would work fine in space. I think normal gunpowder is a fuel mixed with an oxidizer, otherwise it wouldn't burn fast enough. But then I don't know gun technologies, so don't quote me.