No it doesnt matter where you are for the packages. Or if you are frozen. Push the button and all of them are unlocked at once. I dont know about being dead in OT yet. If someone has a chance to try it let me know.
For the car, yea you should have died. For all practical purposes you are just standing there holding a pad driving the car. Just in this case you cannot be shot. If you are dying from Venom (or in other games bleeding out) then heal yourself with a bandage first. Health packs are dropped quite often. If you see one and you dont have a full amount left... I think 3... pick it up.
However, if you actually die it should have respawned you frozen where you turned into a car. Will check that out.