First off i don't think i'm uning the correct terms... but here gos...
For some background reading/terminology, it may be worth having a read through the XDM and X Terminal Mini Howto from the Linux Documentation Project (http://www.linuxdoc.org/). It gives a reasonable (in my opinion - but then I would say that, as I wrote it :) description of the bits involved in configuring remote logons, etc using X and XDM ... May be of some use.
Technically the X terminal software (the bit that runs on the computer you sit at) is called the X server, and the programs you run on the Terminal Server (the Linux box) are called X clients. It's a bit counter-intuitive.
Hmm I wouldn't say that as such - you just have remember that a server serves up resources - in the case of an X server the resources that it is providing are the screen and keyboard/mouse - which it provides to the X clients (the applications).
You can run the Cygwin/XFree86 X server on Windows and it's free software
I have used this - it worked a treat for me. I just downloaded the binary distribution from cygwin.redhat.com and it installed and worked fine 'out of the box'. I even got it doing queries to XDM (running on my LInux box), giving me a complete remote desktop session (seeing KDE running in a Window on my NT machine was very satisfying) - all good stuff. Kevin. (Comments are always welcome - especially contructive criticism or contributions. as that makes things better)