What do the OFF and UP signs mean at station platforms in the UK (or worldwide)?

Answer 1

'OFF' is a repeat signal on platforms to let platform staff know the signal has been pulled off and hence the train is ready to depart. They can check doors are closed, no one making a suicidal attempt to board the moving train, etc. (not that anyone could these days as doors are either sliding doors, or locked before departure).

'UP' is a sign to tell the driver that the signals are set for the up line.