If the KVM tells the PC that the TV has been disconnected, then you can just disable the other screens in the display settings while the TV is connected, and it’ll just work. Which screens are enabled or disabled is remembered depending on the currently connected displays.

No, only when you click on an input field and have it enabled in the system tray

The virtual keyboard is hidden by default, unless you’re using touch. You can change that by setting the KWIN_IM_SHOW_ALWAYS=1 environment variable, until there’s a proper setting for it

You can probably implement it in the script itself, but there’s no external functionality to do it