X11 windows created by root

Just to be sure that you understand the difference between the X11 window and the process that runs in that window.

For the window itself, see the answer of user414777. The process that creates the window (for example xterm) will have additional privileges when run as root.

However, note the differences:

xterm -e bash gives an xterm window with bash. Both bash and xterm run under your own UID.

sudo xterm -e bash will also create a window with bash, but now xterm and bash run as root.

xterm -e sudo bash creates again a window with bash, but now xtermruns under your own UID and bash runs as root.

No.

And if you're actually meaning X11 clients instead of X11 windows, it's still No.

There isn't any concept of privileged X11 clients, they're all equal, and they all have access to any X11 resource.

Any client can do any action on any window, including drawing on it or changing its properties (like its title or icon). Any client can grab the keyboard or the mouse. Any client can fake keyboard or mouse input with the XTest extension.

And any client can kick out another client with XKillClient(3) (not related to the Unix kill(2) system call).