No they do not! For example Front Rotors; if one rotor surface when turned on a lathe will exceed limits of safety (i.e. cutting away more metal from the rotor than is safe as regulated By D.O.T. (Department of Transportation ) then you need to replace the rotor. If the other turns out to only need a small amount of surface removed to make it usable then that can be done. Same thing applies to the rear disc brake rotors. Of course if both rotors are beyond safe resurfacing, then both should be replaced. HOWEVER it is possible that having calipers of a different thickness may cause them to perform differently causing a potential safety issue due to the fact that they will not have the same heat dissipation characteristics. I have not experienced this myself but this does seem to be the basis behind the recommendation of replacing them in pairs. IF I were to worry about then, I would probably only be concerned on wheels involved in steering.
The brake rotors only need to be changed if they are worn beyond allowable specifications and should be changed in pairs. They do not need to be changed with the pads unless they are damaged as above or warped.
Yes you do
You can purchase one or more.
No just the bad one.
Possible that the rear sensors are broken.
It could be that the brake pads are dragging on the rotors.
You can buy just one.
When rotors need to be changed usually the pads have worn down. It is always a good idea to change pads when changing rotors.
Aggressive driving.
mine did the same thing and would not stop until i changed the brake lines also, then it stoped.
You need to bleed the system.
i think your rotars need to be cut