to CF
The answers depend on what recorder you buy and how many decoders it has.
I have a Panasonic DMR-EX77 which has a single freeview decoder, so this is what I can do -
1. if switched to the DVDR scart connection (AV1) I can watch freeview channels, while the DVD is idle.
2. As I have a UHF cable from the DVD to TV, I can also watch terrestrial channels on the standard TV UHF input.
3. If I am recording from Freeview, I can either watch the same on the TV or watch the analogue channels (or watch a VM channel)
4. I also have the VM set top box output into the DVDR and can record from that while watching an analogue program.
What I can't do is watch one freeview and record another.
You can get some DVD (or Freeview HD) recorders that have dual decoders.
Note - none of this will drive your HD screen to full resolution, although the Panasonic drive has an HDMI upscaler (not used myself as main TV is only CRT)
HTH