Qtipia is the graphical front-End (Desktop) on the Zaurus that is based on QT.
If you stripped of all graphical things (Qtopia itself) then you will boot the zaurus into a linux terminal mode. So Qtopia provides the user interface to the underlying Kernel etc.
Qtopia is also used on other linux based devices like the Archos PMA400 etc so they all have the same look and feel.
QT is the language - rather the Graphical widget set that Qtopia uses. So you would be using a C++ language and designing the graphical comonents (like Windows, close buttons, minimise buttons, Tabs etc) using the QT widget set. It is what the MFC are to windows - which provide the Windows look and feel using the windows widget sets (its not called widgets in the windows world).
QT/E I believe is the stripped down to a leaner meaner QT set on the Zaurus.
So QT on your regular desktop would have many more components etc, but the not all are available on the Zaurus - say like the QDateTime class component, QTextEdit, QSplitter etc. These are availbale for the full QT on a Linux box but not there for the Zaurus. So thats QT/Embedded for you.
As a language you could use C/C++ using QT. or use JAVA with some sort of bindings to QT (for the graphical design). I use Python on the Zaurus using PyQt which is the Python bindings to QT.
Perl can be used, but its just perl - there is no QT layer to it - so no graphical components.
PDAXROM - not my territory.
I hope I could get that right - someone correct me if I am wrong.