If you have the 4 whl disc brakes, the rears are probably seized and the front are doing all the stopping, which overheats them and causes rotor warpage, which is the pulsing you feel.
If you do anything check both ends for problems, otherwise if you fix the front it'll be doing it again in a week, and you'll have wasted your money. The rears need to be redone with better than OEM caliper hardware and adequate high-temp silicon based lube on the slides to prevent future problems. Syl-glide is my favorite.
If you look under the back, I'll bet the rear rotors are totally rust on at least one face, having not done anything for some time due to frozen calipers. That's pretty standard with your car.
Agree with the vacuum leak for your selector problem, and the resistor theory sounds right as well. Only high speed uses full system voltage, the others are fractional, so when the resistors go, you only get high speed.