Soldiers stuck as wounded

Cars indeed have a damage threshold, 2 of them, even!

First threshold prevents it from catching fire or exploding. (Pistol hitting a car for example) Then once that one is passed the car catches fire. The second one is where it explodes straight away.

Things to remember when using cars for cover or shooting at them:

• Cars caught fire during your turn explode on your next turn.
• Cars caught fire during an enemy turn explode on their next turn.
• Cover remains after a car blew up!
• You can use grenades and rockets to target and blow up cars before using their cover.
• Kills done by cars are like grenades and rockets they yield no materials only a corpse (fragments)

From what I read, others report that grenades kill cars instantly, where in my games they never do that. It seems higher difficulty is higher threshold. I play impossible so as such I will not note my damage expectations and experiences.

The amount of time spent in the hospital after being wounded depends on the amount of damage you take. This means that healing heavily wounded soldiers with a medkit before they leave the mission will not reduce the amount of sickleave your squaddies get -- what matters is how much they take in, not how much they leave with.

How much damage they can take in without being wounded depends entirely on what armor they're wearing. Armor provides bonus health - if they take more damage than the health bonus provided by the armor, they become wounded.

This means that adding Nano-weave Vests to your soldiers reduces the chance they need hospitalizations, even after being shot, as it gives an additional 2 hitpoints worth of "fleshwounds" they can suffer.

How much "Bonus HP" your units have is shown on the loadout screen - for example, they'll be displayed as HP 10 + 3 (combat armor + nanoweave vest).

In general, there is also an Officer Training School bonus that reduces hospital time.

That said, the simplest answer to your question? Don't get shot. The more damage you take, the longer the time off. Avoid damage as much as possible to minimize hospitalizations.