To receive, decode & record a tv transmission, you will need an appropriate tv card. Since they come in different flavours for different broadcast formats - terrestriial analogue, freeview digital etc. you would need to be careful to choose the right one for your satellite. Dual tuners are widely available and ceratinly within the later iterations of ms media centre, multiple tuners are supported.
Start with Hauppauge, Terratec, Dvico and Pinnacle. Personally, I've always used hauppauge cards and have been very pleased with them.
As for editing, I'm not so certain. My guess would be it could be done with standard editing software, provided it will accept the input file format that your card will use, since tv cards often record into mpeg-2 file format, I can't see why something as basic as Windows movie maker shouldn't fit the bill - again the key would be to do your reading before parting with cash as 'should' is an overused word in computers...
Edit to say: I don't use satellite tv personally, but from memory, I think there may be an issue processing multiple broadcasts simultaneously - I.e. you need a satellite box per channel, which obviously is prohibitive. I could be wrong and things may have changed, but IIRC thta is the case in the uk. Check out the greenbutton.com or av forums for the answers - acres of detail in those places.