Oh, I've got one of these coming up! I've seen the first scouts for that mission.
the acid rain is cherry on the top that all but makes sure I'll suffer some losses.
How so?
I had some dealings with ghouls lately, the mission description informed me about noxious fumes(?) and acid rain. I issued smoke gear and yellow overcoats and that apparently was sufficient protection.
Will Mutant Culling have a more aggressive atmosphere? What even are the effects of acid rain?
now I’m stuck searching for the last remaining [alien]
Many mission enter a "bug hunt mode" after a while, where all aliens' locations become visible on the minimap. Not sure if this one is an exception.
Aliens that have been stunned previously don't strictly have to be dealt with again; at least they don't prevent the mission from finishing. Once you put down the last fresh fighter, all who have previously been unconscious will instantly surrender. That doesn't stop them from picking up weapons and continuing the fight in the mean time, though.
I'm not aware of a toggle to turn off that behavior. Keeping downed enemies down is part of the Piratez experience: manacles exist for a reason (though personally, I only ever tried to use them once. Way too much effort.)
As greattuna said, you can attack prone enemies with ranged weapons. Don't even have to stand right on top. Things get tricky if there are other objects nearby: if the enemy is lying next to (e.g.) a wall, you likely end up attacking the wall instead. In the worst case you have to pick up the body and put it in a place where there can be no misunderstandings.
A few additional beatings with a whip make sure that the enemy stays down for many turns. If whips even work on the enemy in question, that is. But nevermind the details, you get the idea.