it is like those battery powered pendulums..
i would say months.. but it will stop .. its not a perpetual motion machine ..the laws of thermodynamics say there is no such thing..
This is a same idea as "DC brushless motor". But here is a "trigger coil", no Hall-sensor for exact switching. I think, the efficiency also not good (i mean this is a demonstration)
The motor cannot started, but run if the supply voltage exist.
No it would not, there will be power lost (as heat) due to the resistance of the coils and friction in the rotating piece. This power loss cannot be regained, so it will eventually stop.
No, as jrz126 has already pointed out it's impossible, there have been thousands of perpetual motion machine over the centuries - predating electricity by a long time. None have ever worked, you can't generate energy from nothing - all an electric motor does is convert one form of energy (electrical) to another form (mechanical) - the one in question is just a very low power motor. It takes power from the battery and turns, but the mechanical output will be very low, and this means the battery consumption will be low as well.
You already probably have a number of similar devices at home?, battery powered clocks work on a low output motor and low battery consumption.