You certainly couldn't transfer recorded content from box to box in the old days. I doubt that's changed unless you can transfer content via USB stick etc. That's doubtful because you can't even view recorded content on a working box if you ever cancel Sky - the content dies with your subscription.
An old box will work for BBC/ITV/4 channels etc, even the HD ones.
Your old card will work in any box (we used to let the girls take the card to gran's when they stayed over and it worked fine in her Sky box - apart from Sky Sports/Movies. If you have them you will need to get Sky involved.