Hi drüben, welcome to Nosky

It's certainly a bit confusing isn't it?
Well, let's try and break this down.
Freesat isn't really anything new in terms of satellite signal(s), but the hardware is different because it handles the new Freesat EPG properly.
The good news is that you could probably just about receive some - if not all - of the 'Freesat channels' - the bad news is that you would need a large dish. Just how large I'll check for you when I've finished typing this. So no, a Sky minidish would be no good at all.
Getting a card for an old Sky box isn't tough. There's no contract, and no link to a UK address. A one-off payment of £20 for the card, and you're done. No further contact with Sky is required. As I said before though, it's the self-same signal as the Freesat signal, so the reception capability is much the same as any other satellite receiver.
The Sky box doesn't really handle any other satellites, but the Freesat boxes can. Well, when I say that, I can vouch personally for the Humax Foxsat HD box. Flicking between Freesat mode and non-Freesat mode is a bit of a pain, but if you don't do it too often, it's fine. Not sure if all Freesat boxes are the same. I suspect not.
You could almost certainly record to your Topfield from either a Sky box or a Freesat box if you're happy to use the RF or Scart outputs.
A non-Freesat badged receiver will be able to receive the 'Freesat channels' just as well as a Freesat box or a Sky digibox, but it won't give you the nice EPG, and HD stuff or any of the forthcoming interactive features.
Please feel free to ask if any of that is unclear. I'll go check what size dish you'd need, but I don't think you're going to like it!

STICK