If issue #1 is about MangoHUD, you should read its manual to find out how to set the overlay size. If it's not MangoHUD... you should switch to MangoHUD, it's a fantastic application.
Issue #2: Gamescope has built-in support for FSR1 and NIS upscaling. Use this as the launch options: gamescope -W 1920 -H 1080 -w 3840 -h 2160 -F fsr -r 120 -- %command%. This will run the game in a 1080p 120 FPS graphical session, but upscale it to a 4K output resolution using FSR. Unfortunately Gamescope is not perfect and sometimes introduces compatibility and stability issues.
Alternatively, you can use Lossless Scaling for either upscaling or frame generation. It works on Linux and is well-liked, but I've never personally used it.
Issue #3:
The default Proton version is the latest one available. You can set it globally in Steam -> Settings -> Compatibility.
By default, games use the global Proton version. If you want a game to use a different version, you can set it in the game's Properties -> Compatibility by checking the "Force the use [...]" checkbox, then selecting one from the menu.
Regressions can and have happened. Steam offers the latest release of every major version, so if a game needs an older version, you can use it. Older 32-bit games in particular might have issues with Proton 10 or above, but it is possible to downgrade.
You can also use third-party compatibility tools that offer different game-specific fixes. The most popular ones are GE-Proton, Proton-EM, and Dawn Winery (the last one specifically for Chinese gacha games with horrid anti-cheat). You can install them by extracting the archives into the ~/.local/share/Steam/compatibilitytools.d directory.
I strongly recommend consulting ProtonDB if you're having issues with a game.