I would like to use two languages, and testing it works fine. But I can't add a translation for tags, is that right?

Yes, correct, tags are unique keywords different to titles and such as they are used in the url to search directly. If you neede two languages you need to use separate ones for each language. Or maybe combing them like "<lang1> <lang2" would be a solution if it is just two languages.

Another a little inconvenient way would be to pre-/suffix tags like <tag>_lang and the build custom functions to display them according to the language currently set and remove the _lang from the tag for display.

Tags are not translatable for overhead reasons actually.

Then the most simple solution is to just use both languages/tags, like cats/katzen and houses/häuser etc. It's not too annoying for visitors I think when not using too many tags for an image.

Good, then remember to set the search options for tags to partial as it otherwise might not work as expected if searching via the search form.

(German terms or is it in Dutch really the same?)

Ok, thanks for that tip!

Thanks for the tip acrylian, another mark ticked off.
I'll be using method #2.