From my tests - all things being equal - none of those things you mention affect the random number generation. It only uses the next random number when a random number is needed. So if you have three characters with three 50% shots and two miss then one hits, it doesn’t matter which characters you use in which order. Moving doesn’t change anything, since there’s no random chance involved.
Even skills don’t make any difference, as they aren’t using a random value or simply lower your % chance to hit (which could make a previously successful shot fail).
I haven’t tried to figure out if you share random rolls with the enemy, though. For example, if you had one enemy and you took a 50% shot at them and failed and they took a 50% shot at you and succeeded. Could you hide instead and then take the 50% shot at them next round and succeed?
Also, I’m not 100% sure of how they use the random numbers for criticals. They could be pulling a random number off to see if the shot succeeded and then pulling another random number to see if the critical succeeded. They could be skipping the critical check if the first shot fails (sensible). So that could also make things a little harder to understand.
For example, two stalkers shoot and miss 75% shots. Then another stalker shoots and hits on a 50% shot and then succeeds on a 35% critical. That’s potentially 4 random numbers A, B, C and D. Now instead you reload and have the third stalker shoot first. She succeeds on her 75% shot and succeeds on her 80% critical, using random numbers A and B. Now the other stalkers go and take their 50% shots. They could also succeed because random numbers C and D were such great rolls.
So that’s a case where there were the same random numbers will have different outcomes when you have unequal shot %s.