Yes Mandrake 7.0 has KDE, you have to select it during the install. I cant remember if it comes with Mozilla or not, I know it has Konqueror (but it sucks) You can download it if it doesn't ... and I would reccomend going with Opera as your browser choice on Linux.
Updating the kernel ? Do you mean manually changing it or installing updates from mandrake? I'm pretty sure that Mandrake offers and auto update type thing just like windows does so its pretty easy. If you want to build your own kernel thats way behold the scope of this forum and cannot be completely explained in less than a couple pages of text. I would recommend downloading help documents specifically aimed at this, if this is what your looking for, they can be found on http://www.mandrake.com or http://www.linux.com
and I'm sure a few others.
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