In the Dark Knight Returns, Superman looks a lot younger than Batman despite them being contemporaries. It seems that Superman aged a lot slower than the humans around him.

Does Superman's aging work like this is most continuities? How much slower does Superman age compared to most humans? Does he age? Can Superman die of old age? Is Superman technically immortal?

Superman doesn't age (beyond the development of his powers, which started in his teen years) in PC and the main continuities.

Earth-2 Superman (Golden Age) aged like a normal person, with a drastically reduced physical decline. He did eventually retire near the end of Pre Crisis history tho.

Kingdom Come Sups aged naturally but got stronger due to absorbing more sunlight. It's unknown if said aging would reduce the impact of his powers but he is seen to live long enough to see the Legion form. He probably does age but very, very slowly on a actual physical level.

Whatever Happened to the Man of Tomorrow Superman also ages as per normal etc.

Superman from Secret Identity ages completely normally as well, even getting weaker with time

He has to

He went from baby to grown man

The question is does he get old, which depends on the writers and story

Yes.