The doctor in the bunker could heal you, but doesn't. I haven't discovered a way to get him to help you out, period. If one exists, I never found it. As for the bandages, only thing that I ever did about them is wait. They will go away after a certain amount of time. For broken limbs, I believe you can use a doctor's bag to fix those up. That's why I usually keep a medic on my squad. Lastly, to get out of a vehicle, I believe you have to hold down the CTRL button and click on somewhere outside of the vehicle (or on the vehicle; don't remember).

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HAHAHAHA! Your lord of chaos has come, feel my wrath and tremble!!! For the Earth will burn with a fiery light and be purifyed and the corruption of the light will be cleansed with darkness

Here are clear answers for you:
Everything that is red (bandaged etc.) can be healed by some character of yours who has high doctor skills (100). I just kept the good old field doctor of mission 1 in my team till the end.

The doctor needs an ambulance bag (the grey expensive one) to heal every red stuff that bothers you. With the traditional doctors bag (brown) he cannot heal "breathless".

Yes and to quit a vehicle just press Control and the left mouse button next to your hummer.

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Although prepared for martyrdom,
I preferred that it be postponed.
Sir Winston Churchill