First of all, the maximum shutter speed on the EOS-M is one four thousanth of a second. With a Canon 580EXII flash and the EOS-M set to high speed sync, you can use the fastest shutter speed available. There is no PC terminal on the EOS-M so a triggering device would have to be fitted to the hot shoe for strobes.
Yes, but at vastly reduced range and output.
The question was is it a truely electronic shutter. Yes in video mode, it's sensor read off, and I'm not sure in photo mode. Canon have rated the max synch speed at 1/200th, the only physical limitation to this a mechanical shutter, therefore in photo mode it seems likely to be a mechanical shutter.
It's a shame canon couldn't implement a leaf shutter type solution, but then you would still need a conventional shutter for the legacy lenses.
Damned if they do, damned if they don't.