here are a couple of "stumpers" I know.
If the throttle cable breaks, what will happen and how will you safely land the airplane?
Which instruments are mechanicaly driven?
Why do you need to make sure the Primer is in and locked?
What endorsements are required for a C-208 Caravan turboprop?
On the sectional, there are some numbers located on lakes, what do these numbers mean?
How is it possible to fly at an IAS slower than Vso without stalling the airplane?
Is a PPL allowed to fly over a solid layer of clouds on a moonless night?
What part of the POH is "approved" by the FAA, and what part is advisory.
Can you land with a greater crosswind than is shown in the POH.
I'll try to think of a few more
Since Casey threw in his answers, I'll chime in with what I think I know:
If the throttle cable breaks, what will happen and how will you safely land the airplane?
The engine would try to maintain the RPM it had when the cable broke, but due to the engine sucking air and the throttle valve wanting to move toward full open, it would move to full open with nothing to stop it. Also you can use the mixture and carb heat to regulate RPM when the cable broke.
Which instruments are mechanicaly driven?
Along with Casey, I am not sure. They are all mechanically actuated, in a sense, they are driven from something else however; depends what type of instruments you are talking about.
Why do you need to make sure the Primer is in and locked?
So fuel does not seep into the cylinders, although virtually none would anyway even if the primer was not in and locked; on the Cessna it doesn't really push the fuel into the cylinders until the primer knob is pushed back in.
What endorsements are required for a C-208 Caravan turboprop?
The only one I can think of is the High-Performance. I am not sure of the HA endorsement since I don't know the service, or absolute, ceiling of the Caravan. It would not require a Complex though.
On the sectional, there are some numbers located on lakes, what do these numbers mean?
Without looking at the sectional, I believe those are the runway lengths for aircraft to land on with floats (water runways).
How is it possible to fly at an IAS slower than Vso without stalling the airplane?
Slipping is one, and a whole lot of instrument error (which usually happens).
Is a PPL allowed to fly over a solid layer of clouds on a moonless night?
I believe so. The only thing I can recall with a limitation like that is that a student pilot must always maintain visual references with the ground. I can't recall any limitations like that with a PPL cert.
What part of the POH is "approved" by the FAA, and what part is advisory.
No real idea, but not much as I recall.
Can you land with a greater crosswind than is shown in the POH.
Yes, it is not a hard-set limitation, but more of a recomendation that was "demonstrated" by the test pilot during certification of the airplane.