The answer to all your questions is basically yes. You can set up an ad hoc connection using wireless and you probably won`t have to change many settings other than disable the cable connection. A wireless router needs only one cable to the telephone master socket or the cable modem if you are with Telewest for example.
The following link takes you to just one modem/router but it also has 4 ports for cable connections as well. It includes in the bundle a wireless USB adapter which you can use in a spare USB port rather than buy an internal wireless card. You can move this to other computers in the future of course. I find this useful if I have visiting computers that need a broadband connection for updating software etc.
I think that by the time you`ve looked at a seperate internal card and a router you might as go the whole hog and get a unit similar to this in one go.