Hi ThePhotoSoup (?),
and welcome to the forum. No, it's not a dumb question. If you are interested in micro 4/3 gear you have some reading to do and there is plenty of material available. In general all micro 4/3 lenses, be it Panasonic, Olympus, Sigma or the dumb Voigtländer ones, work the same on all bodies.
There are a few exceptions though (a Panasonic 3D lens, some OIS restrictions regarding lenses with no OIS button paired with older bodies, perhaps something more I don't recall at the moment) so checking everything up is a good idea.
The Zuiko 75/1.8 works fine. I don't have a GH3 but I just tried the lens with my old original G1 and everything, including the feature where moving the focusing ring quickly results in a longer "jump" than moving the ring the same amount but more slowly.
If you buy the 75mm for shooting video using a Panasonic camera you should check and perhaps update the lens firmware to v 1.1.