Don't know anything about the TV.
IF it has its own Freeview tuner then you can (or should be able to) watch anything you want to, regardless of what the Box/VCR are up to.
IF not then you can only watch analogue channels 1...5 until switchover, then nothing, unless you use the set top box you've now got. A set Top Box can only receive one programme at a time. You can watch it, record it, or both. But only one programme at a time.
And, yes, it's the EXT or AV input on the VCR you need to use to record from your set top box.
(Hint 1: members may be a lot more able to help if you are specific about makes and models).
(Hint 2: get a PVR.)