When a skeleton has seen me and starts trying to shoot me, it also starts moving side to side to make it harder for me to shoot him. While making this side to side movement, It fell. I would expect that the skeleton stops moving when it would fall, but It didn't.
I will provide a screenshot when The bug happens another time, but that can take some time
That is intentional.
Just like the player and every other creature, they can move while falling, yes.
The fact they fall during strafing is a duplicate of MC-90245.