Focusing on case 3, how would I go about doing this?
In your loop() section just:-
read the sensors
Compare it to the figure you want
If it's above a threshold (plus a bit) then pump up your bag (small pulse)
If it's below the threshold (minus a bit) then pump down your bag (small pulse)
Having that in the loop will just keep on repeating it and eventually you will get to your set threshold. The bit you add or subtract is known as the hysteresis and stops it going up and down all the time. The size of the small pulse on your solenoids will determine how quickly you get to the point you want and the degree of undershoot and over shoot in the system.
do you mean use 2 resistors to drop the vehicle's 14v down to 5v and
Yes but I would count on a maximum voltage of 18V on a 12V car