1. What is prop overspeed?
The propellor "twists" in its mounting to "bite" the air harder, and produce more thrust, or twist the other way to slip through the air easier, producing less thrust - for the same engine RPM. Pour on the fuel, and instead of the engine increasing in revs, like in a car, the prop twists (increases pitch). It's the aeroplane equivalent of gears. A prop overspeed is when the pitch is too fine for the power supplied - and the engine/propellor combination exceeds the engine RPM limits. (Like driving down the road in fourth gear, and accidentally selecting second - the engine screams as it over-revs.)
2. What causes it?
Either a governor failure (the piece of equipment which governs propellor pitch), or in hydraulic systems (which use engine oil or hydraulic fluid to drive the pitch changes), a loss of fluid.
3. How does it affect the aircraft in flight?
Depends on how bad it is, and how quickly the pilot reacts to reduce power. Worse case is a catastrophic engine failure. Best case is a minor limit exceedance, requiring an engine inspection before returning to service. There is a (controllable) yaw when it occurs as well, similar to an engine failure.
4. What corrective action can the flight crew take?
Control the yaw, reduce the power.
5. Is prop overspeed the same as a runaway prop?
I would say so.