Anyone else got the problem that he is unable to change the resolution?

Sys: W10,

Try adding a -resolution parameter on the shortcut.

Just type in: -resolution w h (where 'w' is width and 'h' height)

Okay, but for someone who hasn't ever messed around with this stuff before, where do I type the resolution and how do I get to it?

Right click on the game shortcut > Properties > Path and add it at the very end, after the last ".

I open the properties menu and I don't see a Path option. I see Target, Start in, Shortcut Key, and Comment. I added it into Target such that it looks like this:"C:\GOG Games\Star Wars - Battlefront 2\SWB2Launcher.exe" -resolution 1920 1080
But that still doesn't work.
Adding the resolution parameter to the Start in option throws an error when I click Apply.

What now?

Resolution changes normally. Main menu work only in one esolution - 800x600 or maybe 640x480 only.

You can change main menu resolution if you use a mod like this one https://www.moddb.com/mods/star-wars-battlefront-ii-full-hd-interface