Enemies that shoot at you while moving

I think with modern games it's certainly doable to have the kind of blended animations required to make an actor be moving and attacking at the same time. A lot of games that I've played have soldiers firing whilst running for cover, or flying enemies swooping overhead whilst unleashing an attack. With soldiers or other enemies with guns it's quite easily done - particularly if they're modelled like in TimeSplitters, where they're always holding the gun up, level and ready to fire. Older sprite based games would require individual frames added for these firing movements to stop the enemies sliding around, unless they're just going to do what I did with the LandCarrier in Virus and have the attack come between moving frames. The hard part is enemies that attack like the imp, I imagine. In the new Doom, imps have animations where they're running to the side and flick off three fireballs in quick succession, which looks quite natural. However, I'm assuming that's a specialised animation and behaviour subroutine, rather than them running about and randomly flicking shots off organically, like the enemies in the original Dooms do.

As for your question, yes, in ZDoom you can use DECORATE and ACS to do things like impart or remove momentum from the player in response to actions like firing. I've seen a couple of weapon mods where the recoil of larger weapons pushes the player back a bit. You'd have to check the ZDoom wiki for the specifics, but there's definitely an action to set the player state to TOTALLY_FROZEN or something, which ceases all movement. People use it for cutscenes, so the player isn't running about randomly whilst the camera is doing something else.