So I have endless problems getting the Steam version of KOTOR to run. I have tried many fixes and they don't work. I can't get the mouse to work in the menu and the game crashes after Character creation. None of the fixes work. Does the GOG version function beter than the Steam version?

I don't have the game on Steam, but I do have it on GOG. I've had no issues with it and I currently have it installed on a Windows 10 Pro system with a GTX1080.

Your game crashes after character creation because you haven't disabled "frame buffer effects" in "advanced graphics options". That's "normal". It will work once you've done that. :)