What is KDE application actually?
 

Does it means that KDE application can only be run under KDE ? how about gnome? can a KDE application be cross-compiled into a PDA? what other applications are there beside this KDE app? thanks a lot

KDE apps can run under any environment/window manager as long as the required KDE libraries exist.
That's a bit vague. If you mean "are there alternatives to KDE?" then yes is the answer - Gnome is an alternative. You could also look at the lighter weight managers - Fluxbox, Blackbox, IceWM, etc etc

Basically as XavierP say's.

For example, my desktop/window manager is kde, but I decided to have a try at using evolution instead of kmail for my e-mail client.

This just means that I've got the gtk libraries installed as well as the Qt ones that kde use. As I'm using mandrake 10 as a distro, when I told the package manager that I wanted to install evolution, it went and got the gtk libraries as well as the evolution package i.e. the gtk libraries being dependencies of the evolution package.

If you're like me and a little lazy, I take the easy option and installed kde and gnome - out of habit I usually use kde, but that also means that any of the packages available to me that can work with kde are shown on the start menu.

But no, I don't know if that's a nicety of mandrake or whether it would happen with other distro's without having to do the install's and setup manually.

if i wanted to cross-compile one KDE application so that it can be used in a zaurus PDA, do i need the KDE libraries? where can i get it ? need detail instructions, thanks a bunch

I would use, as a starting point - www.kde.org