Once I disconnect from the mains, can I leave the charger cable in the Mac? I use my MacBook Pro on battery as much as possible, recharging when needed and once a month running it down to recalibrate etc.

However, when the battery is charged to 100% I unplug the charger from the electricity supply and the MacBook from the charger, but I wonder is the latter precaution necessary?

Is there any power exchange between MacBook and charger when the latter is unplugged?

It's not too important but would save me some scrambling around under my desk.
Yes, it's fine to leave it plugged in.
The charger is simply disconnected and there is no closed circuit.