Pretty much yes to all of that, but double check with PC world that the router is OK for BT - they will know, I'm not sure.
There are 2 types, one that you connect to a phone line and do away with the broadband bit you already have, and one that you keep the bit you've got and connect the two with a network cable. As I said, not sure what you need for BT.
Printing - if you have all of the software and files that you want to print stored on the laptop you would 'share' the printer on the desktop.
some help on that...
http://www.microsoft.com/windowsxp/u...utt_july2.mspx
Or, if all of the stuff is on the desktop, you can use a program that you control it from the laptop. You logon to it, and the screen/mouse from your desktop shows up on your laptop. Something like realVNC...
http://www.realvnc.com/
However, you'll have to go through a bit of once only setup stuff to be able to do all of this, so I would think real hard about finding someone good with PC's that will come an do it for you.