I've re-downloaded Mask of Eternity but each time I try to install it there's an error message saying that "Setup has detected that GOG GALAXY is currently running". Help please? Thanks in advance.

Well, seems like you still have the Galaxy process running (in the background) which somehow prevents installing MoE. Try to kill it via the task manager if you can't get rid of it by just exiting/closing the application and see if that helps.

I just did a fresh install via the offline installer and it went through no problems at all, so it's likely that Galaxy (or remnants of Galaxy left on your machine if you had it installed but removed it) is indeed somehow causing the problem.

You could also check the dedicated KQ subforum over here for troubleshooting:
https://www.gog.com/forum/kings_quest_series

I got it. Thanks!