Yes, it is possible, but you cannot do this on-the-fly while playing the game.

1. You need first to put the "prince_translation.dat" file from the English "version" into the "ALL" folder of your German game data folder. You don't have to install the English version to get this file. You can find that identical file on the ScummVM site (the ScummVM team did the English translation for the game), under Game Addons here: https://www.scummvm.org/games/#addons-prince

2. Edit your prince.ini file in your German game data folder and add the following text to the end of the file:
[prince-en]
platform=windows
gameid=prince
description=The Prince and the Coward (w/translation/Windows/English)
language=en
extra=w/translation
path=C:\Games\Galador\
engineid=prince
guioptions=lang_English

Keep in mind, the "path" above should be set to the path of your German game data folder, so it could be different for your specific case.
Save the prince.ini file.

3. Create a copy of the "Launch Galador" shortcut and rename it to "Launch Galador En". You will use this shortcut to launch the game with English subtitles.

4. Finally edit the new shortcut ("Launch Galador En"), by right clicking on it and selecting "Properties".
Set the "Target" field to:
C:\Games\Galador\ScummVM\scummvm.exe -c "..\prince.ini" prince-en

Again note that the subpath "C:\Games\Galador" here also could differ on your case, based on where you installed the German game data.
Press Ok. And that's it.

Use this new shortcut to launch the game with German audio and English text (and UI).

Note, that this can also be done similarly for the Polish installation of the game (Polish audio, English text) but *not* for the Russian installation.

You won't be able to directly share saved games between the two versions of the game though. The all-German version and the German-English version will name their saved games differently. You can of course rename the saved games to match one of the two versions and they should be compatible.

I can't begin to thank you enough for this explanation! My wife is German and we're teaching all three of our young boys how to speak the language, so opportunities like this to utilize games as learning devices is always exciting.

Unfortunately, the English translation could have been a lot better. I think it's great that fans make the effort and I have no doubt it's a ltime-consuming job, but the subtitles really should have proofread by a native English speaker.

I wasn't involved with the translation project, but it is open sourced and maintained over at the weblate platform for ScummVM.

We also had a open beta test period for this game (at least during the road to release 2.5.0) but I think the feedback we got was really small.

Anyone could offer suggestions for improvements if they have some spare time.
https://translations.scummvm.org/engage/scummvm/

Indeed. I ended up spending the last few days improving the English translation. Hopefully the ScummVM team will review it and accept the changes. Fingers crossed!

They did not.

This is not correct. As far as I know the changes were accepted -- I can only see 6 suggestions pending.

However, there has been more progress on this front and ScummVM is working into integrating it to weblate, with the ultimate goal of producing a new improved dat file. I am not sure how much more I can say on this as of yet however, and I'm afraid I don't have an ETA on the update.

I'll try to post here, as soon as I have more news on this, though. Provided that I'm not beaten by GOG themselves updating the game.

Well, then your correction worth that much.

How did you get the German audio? According to the description, that game is supposed to include German audio, but it starts in Polish(?) and there's no way to change the language, neither in the games itself nor in ScummVM.