Trying to avoid confusion...

I'm sure that you can use a tablet for a virtual keyboard and/or a
touchpad component of a desktop computer, but that's not what I'm
asking about.

What if all you have is a tablet and big monitor. Of course what
you see on the tablet screen can be sent to the monitor with a
cable or wireless.

But...

Can you use a tablet as a virtual keyboard and/or a touchpad while
displaying the contents of the tablet, the GUI output part like
windows and dialogs that we interact with, on a PC monitor? The
idea is to make better use of the tablet touchscreen while using
the PC monitor as if it were connected to a PC. Preferably for
Android, but curious to know if it's been done on an iPad.

It might be tough to do since the iPad/Android touch interface
uses the whole screen of the tablet. Functioning as a touchpad, it
would control a pointer like on a PC, so you would have a pointer
moving around on an iPad/android GUI, which is even more involved.
Yet I have seen what looks like a pointer on an Android GUI, maybe
that's related.