Running a pseudoterminal inside a pseudoterminal

I'm trying to understand how the programs like screen and script control I/O.

My knowledge of terminal, tty etc. comes from reading the 'tty demystified' article, and all the SE answers I could find. So from what I understand, roughly the interactions between components work as follows:

Console(Keyboard+Screen) ---- xterm(pty master) ----- tty line discipline ---- bash/other programs(pty slave)

where the line discipline is in the kernel, and xterm and bash run in the userspace.

1. Is this correct?

Now, when we consider programs like screen, script, they are userspace programs that run in a terminal(the existing xterm), yet are able to control I/O to/from other programs. The article mentions that this is becuase they run another pseudoterminal inside xterm(the existing pseudoterminal).

2. Does that mean that they open up a new pty master - slave pair, control the master end of this new pair, and all the processes launched from them run on the new pty slave? For example each time I start a new 'screen', and run the tty command, it shows me a diffrent /dev/pts/x. Does script also run in a similar way?

3. Finally can somebody point me to any article/book where I can get a little more detail on this stuff(Haven't been able to find anything)?

I'd also like to reference this answer, though it is very brief.