I've got the DMR-EX85EB linked to a Toshiba LCD.
Yes you can watch one digital program whilst recording another.
The RF aerial goes into the DMR-EX75EB then loops through to the TV. In addition I have a HDMI cable between the DMR-EX85EB and the TV.
The DMR-EX75EB is a fantastic and very versatile piece of kit, I'm sure you will be very pleased with it.
As for the Sat receiver I'm afraid I can't comment but it is covered in the manual.. And there have been threads on this forum about it, maybe a search will come up with something?