I thank you dearly for taking the time to test the Linux version and write your feedback ➰
As you might guess, I only have a Windows computer and have taken Linux and MacOS exports thanks to Unity's multiplatform builds on its Windows editor. They are not tested at all!
Unfortunately, I have no idea how to fix the fullscreen toggle issue at the moment. However, since it might work on some Linux distributions, I would not delete the button.
I have published a small patch that might fix your issue with the exit button. (I programmed it to forcefully kill the process instead of going through Unity's quitting sequence when running on any Linux platform).
Could you be generous to test it out and inform me if it works or not?