In answer to your questions - a normal freeview box won't work with Freesat. A Freesat box connects to your satellite dish in the same way as your current Sky box - no extra cables.
I am not sure about your Sky "new card" business, but you know that Sky do a Freesat card costing just £20 (for those already with Sky Digital equipment).
"Q. I already have Sky digital satellite equipment - what else do I need?
A: All you need to gain access to the free channels available on the digital satellite platform is a Freesat from Sky viewing card, which costs just £20. If you’d like to access the interactive services available, you’ll also need a working phone line. To purchase a viewing card please phone Sky on 08448 244 400."
http://www.freesatfromsky.co.uk/faqs-freesat.aspx#q3
@ Bob's answer: "Freesat from Sky gives you access to a great choice of over 240 quality digital TV channels, including terrestrial channels like BBC1, ITV and More4 and Sky3 – that’s four times more than Freeview TV. And with channels ranging from entertainment to sport and music, including shows like Cold Case and Shear Genius, there’s something for everyone to enjoy."
http://www.freesatfromsky.co.uk/freesat-tv-choice-all.aspx
For a comparison - Freesat from Sky vs Freesat vs Freeview , check out:
http://www.freesatfromsky.co.uk/freesat-how-it-compares.aspx