Is there a button to open the roof on the key fob? (with the engine off)

It depends on the year of the car, on my 2003 model, l just keep the unlock button on the remote pressed down and the roof opens,

Andy

Press the unlock button once, the driver side door will open. Press it twice all doors will open. Press and hold it a third time and the windows will roll down and the top will come down as well. Granted a new enough BMW ( l believe 2000 and up).

Yes - but the convenience opening function has to be activated by the dealer first. This function is deactivated from the factory to prevent unintended opening during transport.
Also - try and limit the use of this function as it puts a severe drain on the battery.