Ah, in Germany they do of course do the third thing, and they're also involved with safety around the stadium, which in the case of, say, Dortmund - Schalke is a major operation. I don't think they're involved with the actual match action though.

Oh, and here the state pays for it, which is an issue of some conflict. Problematic matches can cost huge sums, and there are calls to make the league pay for it.