Fines are neither extrajudicial nor cruel and unusual. It's in everyone's interest for you to pay a fine if you don't file your taxes than for you to receive a prison sentence.
Again, it's rare. The state is financed via very high taxes in Germany, not by abusing fines as a money grab. Some local admins get overzealous with speeding + parking violations, but even that is pretty cheap. And what's the alternative? Would you prefer your car to be towed and your license invalidated? Paying 20€ is cheaper for everyone involved ... and if you're really allergic to paying money and the picture isn't perfect, you can usually get out of it by claiming "that person could be anyone".
Police beating up innocents also happens rarely in the US.