(like how can I access on-line a record of my recent journeys, what if I touch in at a Zone 1
station when my Oystercard has only a couple of pounds of credit left, but travel to a zone where
the fare would have been more than that - can I top up at the destination or not).

The barriers will only open if you have enough credit to make the cheapest
journey possible from your starting station. This is £1 from most stations
and £1.50 in Zone 1.

When you arrive at the destination you will be allowed out through the
barriers and the balance will become negative. You are not allowed back
in until you top-up again.