So long as you have someone standing up to attract the heavy launcher missiles...
I generally manage to distract myself from the not-prone thing, but this time, with two ranks, guarding a narrow entrance, at close range, I can't help but suspect that the front rank were too close to really run away from whatever was coming down the elevator, and could have been shot by their friends. Meh, it was just particularly noticeable, but really not an issue.
Stunning works gradually on the life bar. Your health goes down and your stunning goes up. If they meet, then you fall unconscious. Some critters go down quickly but some of them have ship-loads of health and stunning weapons don't do that much damage, and stunning wears of over time. So yes, stunning can work much faster if combined with shooting. I generally play turn-based, and some things have varied effectiveness between turn-based and real-time, but I always found frag grenades to be weak, and very dependant upon how close to the detonation the target was, and tended to blow up valuable loot, while stun grenades would reliably take down basic targets who didn't immediately exit the area of effect. Stun smoke also clears quickly, so it can be useful for clearing smoke, as you can only have one air effect in any given tile, so the stun gas replaces the smoke.