I tried to customise the controls with my Xbox controller but it seems to have set some weird mappings that I can't clear out. For example, the left-right on the main screen (go to Hangar or Stats) seems to be reversed. Also sometimes pressing the Option key on the keyboard closes the game. It also doesn't seem to remember full-screen mode and starts windowed every time.

Is there any way to reset the control options to their default values? And also to get the game to remember to start full-screened?

For reseting - Windows: Navigate to %APPDATA%/.LUFTRAUSERS/ and delete the file input0.txt
OSX/Linux: Open a terminal and type: mv ~/.LUFTRAUSERS/input0.txt ~/.LUFTRAUSERS/input0.txt.2
Looking for solution to your problem with Fullscreen.

edit: you're probably using an outdated (or not Windows) version , this is what I found - "The fullscreen option is now persistent in the latest Windows build."
https://steamcommunity.com/app/233150/discussions/0/558750985815540869/

Thanks, I'll do that! I'm using the latest GOG version for Windows. I wonder if that's out of date here?

EDIT: I've just PM'd Judas about whether GOG has the latest edition.

No idea, but you can also try editing config file, which should be in the same place as input0.txt.

Apart from the input0.txt file, I only found a save file in that location. Maybe this is an old edition. We'll see what Judas says.