I've been watching the wounded and dead as I play practice quick battles with all of these same questions in mind.
I can't say for certain, but I'm pretty sure I watched a wounded soldier die the instant before a trooper got there to give buddy aid.
I also know for sure I had several wounded guys laying in a spot where an arty barrage had hit nearby and I watched a subsequent direct hit wipe them all out. If I remember right, even their bodies were gone.
I read in the rules somewhere that at the end of the battle, your score is increased directly by the amount of aid you have given to your wounded and dead. In other words, those you've cared for do not count as heavily against you. While those that you have not cared for are listed as MIA and count against you strongly.
Further, I'm not positive, but I think I noticed on a couple of instances that I took care of a couple of wounded men and instead of disappearing from the board as if they had been rushed off to the hospital, they rejoined their unit, because apparently they weren't wounded all that badly after all. Sissies. But seriously, I'm wondering if their base is yellow when they will rejoin their unit after buddy aid and red if they go to the hospital after buddy aid. I have no confirmation of this. When I see someone has a yellow base or a red base and give them buddy aid, by the time I get to the next turn and they are taken care of, I have always forgotten what color their base was.
I've also noticed that once a unit has a wounded soldier in it, that soldier moves somewhat slower and sometimes a lot slower than his fellow soldiers in his unit and tends to drag behind them. I would suspect that he is also handicapped in his fighting ability.
It takes one soldier one minute to give buddy aid. Obviously this is a ridiculously short time (unless they are dead). I think that is because medics are accounted for in the game abstractly. I think buddy aid mostly represents getting the wounded to a medic who are assumed to be present on the battlefield. It's nominal care, like dragging them out of the line of fire so a medic can treat them, or sometimes maybe a quick patch, or just being with them for a few moments and reassuring them while they intermittently scream for a medic and make sure the medic finds his way to them. The designers just chose not to make the game about medics and transporting the wounded to the field hospitals, but there needs to be something in the game to represent the distraction the wounded cause to the fighting unit.
It's impossible to say whether taking care of the wounded increases the overall survival rate of soldiers without playing a lot of games both ways and averaging the results to see the differences. But I think all indications are that it does, especially if I was correct in seeing that one died on my way to give them buddy aid. I think the rules also allude to that.
I think Juju's mods with the red and white crosses representing the wounded do make it easier to see who needs taking care of, but to spot every dead and wounded soldier, I have to cycle through all units and even then it is sometimes next to impossible to know where their actual pixel body is lying.
So I agree, something needs to be done to make that easier. Like you say, enlarging the wounded bodies would help. So it would be great to have an Alt+something key that would enlarge bodies of the just the dead and wounded and make them turn a bright red or yellow. Or maybe be able to buy a medic team armed with a bloodhound. jk
I also think making the dead have a brown circle for a base was a bad idea, because it doesn't stand out enough to make it apparent from the other terrain. A lot of the time, to me they look like they are not even selected. I scan right over them.
Another problem I can't figure out in giving buddy aid, is that the wounded always seem to be lying at a vertex between four spaces and I often can't figure out which space I have to send the one giving aid to in order to care for them. It seems like I have more success if I plan their movement path such that they have to step over the wounded laying at the vertex between the four spaces. Or sometimes, the intended aid giving soldier just keeps lying on the ground or sitting around next to the wounded and I can't get them to administer aid. So that continues to perplex me.
I've tried to decide what is the best tactic to have someone handy to take care of the wounded, while the rest of the unit goes on with fighting. Since it's important to have some sort of armor hunting team with your platoons, but they usually are deployed a little to the rear or sides, I've been using those as medic teams, or scouts or rarely snipers, or sometimes battalion leaders or their aids. The main ones I try to have taking care of wounded are the crews from destroyed vehicles or guns and trucks that aren't being used. Also teams from split squads who've been so shot up they are nearly useless, because they will panic the next time anyone shoots at them, yet they are still front line troops, so they are useful in following the front in good cover, caring for wounded.