Generally pad material transfer to the rotor is desirable, it increases the friction coefficient and is partly why new brakes on fresh rotors don't work so well at first.

There is a chance that the last set of pads had a material that is incomparable with the newer pads but there really isn't a way to tell. Some 80 grit sand paper could be used to clean both sides of the rotor, don't expect to get much of an even looking surface, it will be lots of work. Hard brake material can also make noise.

Pad shims are usually coated aluminum to prevent squeaking between the pad back and caliper piston.

If there are outlines of the brake pad around the rotor, this is sign of repeated hard brake use then sitting stationary for a period of time. ( running road course time trails, coming off the track hot then parking the car.) This might cause noise but usually results in thumping when the brakes are applied.

Sometimes the caliper does not have enough mass damping and will squeak no matter what you do. I've read that on the R129 bodied SL600 aluminum calipers were prone to noise at more than 1/2 pad wear, moving to steel calipers added more mass and took the system out of resonance. It might be worth looking for a service bulletin.