May a Cessna 182 land on a major, high-traffic airport, say EDDF (Frankfurt)? Some 30 years ago a family's friend owned a TR-182 Skylane (Turbo,
retractable gear) and we sometimes flew around here in the Rhine-Main
area around Frankfurt. Of course he used EDFE (Egelsbach) for take-off
and landing. I remember asking him if it would be possible/legal to land
in Frankfurt with his Cessna 182.

As I recall, he said they would likely reject such a landing as they
wouldn't really appreciate us occupying a runway and make the big planes
wait for our tiny one. Even if we were allowed, the landing and parking
fees would be in such high regions that no one in their right mind would
be willing to pay them.

The only exception, he said, would be an emergency. In that case we
could very well land in Frankfurt but must be prepared for massive
interrogation afterwards if the emergency wasn't obvious.

I'm not asking about a C182 specifically but about "small" GA planes 
(say MTOW below 2-3 t) on "big" German airports such as Frankfurt.
There is the General Aviation Terminal (GAT) in Frankfurt that is handling "executive and private aviation flights" as they say. General aviation airplanes and helicopters are handled at this GAT that is open 24 hours per day. I think the best is to contact them.

Some additional rules related to GA in Frankfurt can be found here. Bus service is mandatory for passengers between aircraft and GAT. The list of services includes a sentence Lashing of small aircraft. So probably some not very big are expected to arrive.

Landing fees in this airport are used solely to refinance airport infrastructures and the resulting operating expenses. They are regulated, and, while not exactly very cheap, they are not astronomic either.