I am not able to run Star Control 2 on my Mac with Catalina. I open it and nothing happens. Is this a known issue with Catalina's lack of support for 32 bit programs?

Yes and no. The game runs in a DOS emulator. GOG used to use emulators running in 32bit but are working on moving the DOS games to use a 64bit emulator. You can yourself change the bundled emulator to a new 64bit version, if you are technical enough.

Thank you. Do you know a good source of instructions on how to change the emulator?

Sorry no. Search the general forums or the wide internet.