I checked instructions in WSGF http://www.wsgf.org/dr/homeworld but I don't have that key. Also whenever I set resolution in the homeworld options it always resets after next start. Is the game broken or what? Any way to actually change the resolution and to have it permanent or is this version gimped?

Thank You very much. That helped although I cannot run it through GOG Galaxy Homeworld Launcher since it crashes when it is set to Administrator mode. Game needs to run through shortcut without using Galaxy Client.

The GOG Galaxy client is known to be problematic with older games like this, I don't recommend using it and running directly from the shortcut instead, as you've done :)