The hard drive died on our Windows 2k server, fortunately I have a good backup on an external hard drive made with Windows Backup. If I re-install a minimal copy of 2K from the setup CD, can I restore everything from my backup or are there files Windows won't overwrite with the OS running? If I mount the replacement hard drive as slave in an XP machine, can I use XP's Backup software to restore the image of the old disk without re-installing 2K from the CD, Product key and activation, etc?

Can I run CHKDSK from one NT based version of Windows on an NTFS disk created with another flavor of NT? I went in to check the server on the weekend, the 2K install CD's were locked in the vault, so I couldn't run CHKDSK from the 2k Recovery Console. Wouldn't XP's CHKDSK render the exact same result? MS's Knowledge Base says to use only the 2K version of CHKDSK on a 2K drive, but I assume those documents were written before the release of XP.

It has been years since I used any MS bckup functions but if memory serves me correctly the OS needed to be up and running. If that is the case then you would need to have an install CD and key. Again, if memory serves correctly the restore files can be used selectively. That is pick and choose what and where to restore. If I am correct, which I don't guarantee, then you would get Windows running and then use the restore file to restore programs and other files.
I suggest you try some search terms on the Micrsoft Knowledge Base to learn more on what can be done with a restore set.