must brake rotors be replaced with pads?

Yes , the rotors should also be changed , The glazed surface of the rotor and its' " trueness " are important . After a few hundred brake jobs you learn certain steps to take so that you don't have a problem and don't have to pull it apart again .

This is always a contentious debate, if the steering wheel shakes when braking or the thickness is at minimum then yes do the rotors at the same time. Normally you will go through two sets of front brakes to one set of rear brakes but the rears should be checked every time the fronts are done. And don’t forget about flushing the brake fluid. On all my vehicles I flushed the entire system will full synthetic brake fluid, it cost a bit but once it’s done you hardly ever need it flushed again unless it gets contaminated.

Yes, If not replaced, at least re-machined to make sure you have an even and true surface otherwise they will eat up the new pads and you'll have vibration on the wheels because rotors get worped with the heat.

Plus there's a minimum thickness, or discard, specification stamped on the rotors. If the rotors are worn to that point, very close to that point, or beyond that point, they must be replaced. If the rear brakes are still good, no repairs are needed. But the rears should be inspected to be sure. Hope that helps! Jim