Hi Kwicky,
To answer your first question, no not if you buy a digital tv receiver.
As VHG points out the current setup of being able to watch one thing and record another is because both the VHS and TV each have a separate tuner.
If you want to watch and record digital tv you will need two digital receivers, one for the tv and one for the recorder.
A lot of PVRs and some sat boxes have twin tuners allowing you to record and watch two different digital channels at the same time.
To answer your last question, analogue terrestrial gives us five tv channels whilst digital offers around 40 tv channels and a number of radio channels all without a subscription. Do you think that's a bad deal or not?