But it all seems quite complicated; is it true that in some regions it is mandatory to take home all fishes?

Yes, I'm from Germany.

Short answer: As far as I know there's (aside from put&take trout lakes) no obligation to bag every fish in any water body in Germany.

Long answer (and and a digression on why things are the way they are here right now):

In Germany, the debate over fishing centers largely on the Animal Welfare Act, which, according to its wording, prohibits: “Inflicting pain or suffering on an animal without a reasonable cause.”

The key issue here is the “reasonable cause.” Catching fish for food (i.e., to eat) is generally considered a reasonable cause. However, according to court rulings, catching a fish just for the sake of catching it and taking a few nice photos is not a “reasonable cause” and is therefore prohibited under the Animal Welfare Act (which, ironically, tends to result in more fish having to be killed here)

What matters here is the intent to catch a fish solely for the purpose of releasing it. In all other cases (fish too large—cannot be used, actually intended to catch a different species, etc., etc.), releasing a catch is not a legal issue. An exception is non-native/invasive species (which sometimes include catfish): In these cases, returning them to the water (and thus releasing them) is actually prohibited under national law (and also under EU law for blacklisted species).

If you want to fish in Germany, I’d generally say, “No plaintiff, no judge.” You should just avoid deliberately catching fish for photos—and then releasing them—in places with lots of onlookers.

In general, I can also recommend Germany as a fishing destination; however, in this country (partly due to the legal situation and high population density), there tends to be a higher catch rate, which makes fishing in public waters with a guest permit a bit more difficult.

Fly fishing and trout fishing in the low-mountain rivers and streams or in the Alps is something I would definitely recommend.