1) Does the built-in tuner only get BBC1 / BBC2 / ITV / C4 and five? If it gets NOTHING else at all, it's unlikely to be digital (and therefore analogue). When you go into text from that tuner, does it look like 'old style' Ceefax/Teletext or does a bar appear with nice clean/clear text, filling about the rightmost third of the screen? ...Or easier still, what's the model number of the telly?
2) A digital tuner built in a telly is 99% of the time Freeview, the other 1% of the time Freesat. If it doesn't have either of these, it's most likely analogue only (built-in).
3) Freesat carries most of the channels on Freeview (but not all), and a few others which aren't on Freeview (although how much there is on them worth watching is very much debatable). FreesatHD carries BBC HD, ITV HD (neither broadcast 24/7, but there's worth-watching stuff on both regularly enough), and also Luxe TV HD - I've never once seen anything worth watching on that one.
4) If you're connecting a Foxsat HD box (receiving FreesatHD), it will have HDMI output, that means a) high definition channels will be displayed on the TV in high-definition (normally 720p), and b) non-HD channels will be upscaled from their native 480i resolution to 720p resolution by the chip in the Humax FoxsatHD unit - as above, this does a fairly reasonable job of upscaling - and you can expect it to look around the same as your Sky probably does.
5) You can use the same dish for Sky and Freesat, you just need enough LNB connections. If you've got Sky+, you've got at least a twin-LNB (one Sky+ box needs two connections to the dish), and very often Sky engineers install a quad LNB because it's just easier. In that case (and so long as you've not got other Sky boxes elsewhere in the house), you'd have two LNB connections free for a Freesat(/HD) PVR. If you've a twin LNB you can replace that with a quad for under £20 and just run the cables; if you've a quad with two free connections you just need to run some cable and plug a Freesat(/HD) box/PVR into the end of them. ...Word of warning by the way, always disconnect the power from Sky/Freesat boxes before messing around with LNB (dish) connections - failure to do so could lead you to blow up the LNB (there's no exciting fireworks, but you'll have no signal).
6) I still don't understand how having a Sky+ box connected on a SCART, and a Freesat box connected on HDMI (in the case of Freesat HD), or another SCART (even chained through the Sky+ box if required), FORCES you to no use the inbuilt tuner? So long as you've still got an antenna plugged into it, there's no reason you couldn't still use it (if you wished).
All the best,
Rob.