Boy they're some good questions for someone who has not flown in an airline alright!
I haven't got much to add to what the others have said except that often pilots will have their ownequivilent of FREDA checks that aren't written down in the Airlines SOP's and apply to most airliners. When I first started flying the 737 a training Captain told me to mentally run a check every few minutes that was TRRAILS FP,
Thrust, Rudder,Radar, Anti-ice, Ignition, Lights, Seatbelts, Fuel, Pressurization.
When I write it down like that it seems a bit unweildly, but regardless, I took his advice and started to do that as a new F/O doing short sectors on older 300's and 400's. It quickly became a sort of scan pattern that I did and didn't really have to think about because of repitition and I would often find myself picking up a missed switch earlier than I otherwise would have. I remember picking up that the pressurization system was keeping the aircraft 'on the ground' and the diff was increasing rapidly one time soon after we got airborne in Singapore. Over the years I've modified it slightly to include Traffic (ie TCAS) and Transition in order to ensure I haven't forgotten either of those things. I'm on a different type now but still use it. I'm not suggesting that it's a particularly good acronym (I don't even think of it as an acronym now), just that many airline pilots will do an equivilent of FREDA after takeoff and every few minutes for the rest f the flight.
Enjoy flying your Pipers, I would like to swap for a day
