Yes to both questions. You can fit an LNB switch (crude method) or fit a twin-output (or quad-output) LNB to your dish.
See
http://www.satcure.co.uk/tech
Click on Page 10 button for quad-output LNB info.
(Lots more info on this site).
If you share the card between two Sky Digiboxes, the box which does not "own" the card will have a very limited channel selection.
But if you don't want both boxes on at the same time, your simplest option is to keep the Digibox as it is and simply connect RF Output 2 to your upstairs TV set with suitable cable. If you want to control the Digibox from upstairs, use some form of remote extender such as a "DigiLink" or a "PowerMid".
Or, if you don't want cables, there are wireless systems to transmit picture, sound and remote control signals. See
http://www.satcure.co.uk/accs/page3.htm
Fman