sudoers right are necessary for updating the udev rules, that we use to detect the boards.
Mbed Studio is still installed in /root/.local/bin because we prefer it to be installed exclusevely for the user running the installer. This is also necessary because some internal modules need to be compatible with what we do on other platforms, like Windows.
As I mentioned before, at the moment only Ubuntu 16.04 and 18.04 are supported. We are already working to support Ubuntu 20.04, but due to some third party software (like clangd) this requires us some effort.
The fact that you see the AppImage in the wrong folder (/root/.local/bin) is due to a change in how the newer versions of Ubuntu treat the the $HOME variable when sudo rights are used by the users. You can find more information at https://askubuntu.com/questions/1186999/how-does-sudo-handle-home-differently-since-19-10.
I hope this clarifies what you are seeing.
Federico - Mbed Studio team