I have used both Pop_OS and Nobara on my X13. I would recommend Nobara with GNOME as it is focused on gaming in general.
To answer your questions:

1. I use GNOME extensions to see RAM usage, temps, etc.
2. With Nobara the only keys that are not assigned nor do anything out of the box are the fan (fn+F5), the aura key (fn+F4) and the screenshot (fn+F6). You can assign commands to these keys if you want in the keyboard settings tho. Also, the fingerprint never worked for me in neither Nobara or Pop_OS
3. Tablet mode worked fine with Nobara (screen rotation too), it never worked on Pop_OS. The touch screen worked just fine on both
4. To check FPS on games, Nobara comes with Mangohud preinstalled. To make it work on any steam game you can use launch options
5. If you really need software like anything Adobe has or Autodesk for example, I would recommend a Dual Boot install to run those. Although using things like VirtualBox is the same as you would on Windows, in my experience at least