For example, can the Boxes be set to record one TV Channel continuously over 24 hours x 365 days, even if apparently in Stand-by, apart from being able to be set to record various series and the like, which could build up to be virtually full time?
No - on demand doesnt give the facility to set advance recordings in the same manner that you do with satellite programmes.
On demand only shows you lists of programmes that can be downloaded now and when one is chosen it will be downloaded "now" but it is a background task which is visible in the planner.
If I was the OP the first thing I would try is to reboot the box. They are very old technology and not at all reliable.
BT Infinity 2 - IP profile 77 / 20 - super fast!
Previously BE Unlimited - 21,000 Download 1,200 Upload but then moved house - 6,500 Down, 1Mb/s up - gutted!
Ex <n>ildram , been to SKY MAX - 15,225 Download