1- After engine start the starter engaged warning light remains lit. The correct action would be :
a) continue with the after start check as this is normal.
b) wait 60 seconds and shut down if the light is still on.
c) shut down immediately.
d) shut down within 30 seconds.
In this condition the engine is driving the starter motor. Because of the gear ratio (small pinion gear on starter motor and a very large ring gear on the engine) , it will be driving the starter motor at very high RPM. Yopu must shut down immediately to avoid the ring gear and starter moter from being seriously damaged. Option c.
2- An ignition switch which is shorted out at one magneto would result in :
a) the generator being tripped off line.
b) inabilitu of the engine to start.
c) inability of the engine to stop.
d) a dead cut when the other magneto is switched off.
We shut down a magneto by using the ignition switch to earth its primary circuit. If the ignition switch for one of the magnetos is shorted to earth, then that magneto will not operate. So when you switch off the other magneto (or when it fails in flight) the engine will stop. Option d.
3- "Superfine" pitch on a turbine powered aircraft :
a) provides more power at high altitude.
b) aids in windmilling and relighting the engine.
c) provides more power at low altitude.
d) require less power for starting.
I have already answered this question today in a separate thread.