The main distribution site for KDE is ftp.kde.org. However, this site is often under heavy load, so you might prefer one of the KDE mirror sites. You can find an up-to-date list of KDE mirrors here.
Yes, major Linux® distributions already ship KDE. As building a distribution takes some time, they might not always contain the latest version, but for a start or to avoid downloading from the Internet, they do provide a good starting point.
You can find an up-to-date list of distributions that ship with KDE here.
Currently, the latest stable version is 2.0.1.
The KDE 2.0 Info Page contains a lot of information specific to this long-awaited release.
You can get the latest snapshots from ftp://ftp.kde.org/pub/kde/unstable/CVS/snapshots. You might also want to consider setting up your own CVS client in order to maintain the latest snapshot at all times. Please refer to How to use cvsup to get KDE on doing that.
By the way, if you want to know what CVS is, please refer to What is CVS?.
Qt™ is a product of a Norwegian company, Troll Tech. You can always get the latest Qt™ version from their FTP server.
However, you should also be able to get Qt™ from the above-mentioned KDE sites. And with most up-to-date Linux® distributions, Qt™ is already included. Please see Q: 4.3. for the version of Qt™ you need.
Qt™ is a C++-based class library to build user interfaces. It provides most of the widgets you will see in a KDE application: menus, buttons, sliders, etc. Qt™ is a cross-platform library that allows you to write code that will compile on UNIX® systems as well as Windows®. You can learn more about Qt™ at http://www.troll.no.