So, as the title says, the game crashes when I try to load level 6.
I finish the 5th level, then put a point in Force Speed (the only available Force power at the moment) and click "ok" to continue with the game, but after the loading the game crashes to desktop, where every icon is like 4 times bigger than they should be until I restart Windows.

I play the game on Windows 10 and I had no problem with the game before this one, it ran smoothly and I had no crashes whatsoever.
I tried searching for another thread here hoping to find a way to fix the crash, and found another one that had the same problem I'm having (except for him it happened at level 8, not 6), but the only answer there doesn't help me.

Anyone knows a way to fix it?

I'd try change the compatibility settings for JK.exe to Windows XP (Service Pack 3).

Another possible solution is to use dgVoodoo 2 wrapper:
- download the latest version from here;
- extract dgVoodooCpl.exe, D3DImm.dll and DDraw.dll into the game's main folder;
- run dgVoodooCpl.exe from your game folder;
- click on the ".\" button in the upper right corner of the dgVoodoo Control Panel to set the config folder to the game folder;
- switch to the DirectX tab and disable dgVoodoo Watermark near the bottom;
- click "OK" to accept changes.
Now you are ready to run the game.

As dr.schielmann suggested, it could due to GOG's compatibility settings. You can try removing them with a registry file that I uploaded some time ago:

http://s000.tinyupload.com/index.php?file_id=13336490385949960712

It says that it's for fixing missing music in the game, but it fixes the music by removing the compatibility settings (that I've found are completely unneeded in Windows 10 and only cause problems), the same ones that could be your problem. If it doesn't solve your problem and you happen to want the compatibility settings back, you can simply re-install the game.