Note that there's the scroll_maximize_restore advanced option, which allows to do what you're asking for by using the mouse wheel.

Unfortunately, I am having trouble finding a way to identify the window of the Taskbar button that has been clicked (I cannot get its handle), so I have not been able to write an AHK script to do that.

You might want to try using 7+ Taskbar Tweaking Library :)

I will add maximize/restore in the next version. That's not exactly what the OP asks for, though: he asks for one hotkey to be able to toggle between maximized/restored state, as far as I understand.

Newer versions include an error code along with the "Could not load library" message. What error number are you getting?

That's already possible, please see the FAQ here.

Seems like a duplicate of this issue, with a slightly different scenario:
http://tweaker.userecho.com/topic/308231-cycle-between-taskbar-buttons-stops-half-way-in-windows-8x/

Looks like a duplicate of this:
http://tweaker.userecho.com/topic/164567-custom-date-format/

And indeed, there are tools which provide similar functionality.
In addition to the one you mentioned, there's also T-Clock, which you might want to try out.

As far as I remember, the hotkeys are global, i.e. it won't be possible to reuse the code for a single button group in a straight forward way.

I'm not sure, but I think that it has to do with the system visual theme.
Also, there's a topic about it already, so closing as a duplicate:
http://tweaker.userecho.com/topic/406829-/

What is your definition of "in focus"? You already can choose to skip minimized windows.