1. Undesireable, but unavoidable. The gears may not have been fully meshed, it happens.
2. @
mankarn86 got it, this is called lugging. I've always heard it increases knock which can cause damage in the long term, but in a modern engine with knock sensors it's probably harmless. You'll get the hang of it.
3. Speaking from other MT's I've driven, this will never happen unless you are pushing on the gear shifter while giving it a tiny amount of throttle. Any situation where you are giving it -just- the right amount of gas so that if the engine was disconnected from the transmission it would be losing rpms at the same rate as the transmission is from drag & friction, it will pop out with just a flick of the wrist. If you do this by accident, just clutch in and put it back in gear.
I suggest doing this on purpose once just to learn what to expect. Get your car up to speed, lightly press towards neutral, and slowly let up on the throttle.