EFATO and Cowl Flaps
About 50 to 100 fpm I think, noticeable during normal operations. However the engine will very quickly build up temps with the cowl flaps closed, if you do close the live engine flaps monitor the temps. I would leave the live engine flaps open, best to keep your only friend as happy as possible. Definately close the dead engine ones when time permits.
I understand some PA31-310's only have one hydraulic pump
Aztec problem not the PA31 series, all the Navajos and Chieftains had the same problematic gear system, with some minor differences in cabling vs pushrods. There is no way to release the uplocks if your hydraulic fluid is lost, no matter how many pumps you have (engine, hand or ram air) the gear remains firmly up and locked. The up and down locks are very fickle and require good pre-flight and maintenance checking to prevent problems.
Have had two occurances of this both during pre-flight checks in later models which prevent flap actuation if a split is detected. Both were due to the screw jack threading. In the earlier models (pre 1975 i think) the assy flap protection only worked if the flap assymetry started from flap zero or retracting from full flap, if occuring from an intermediate point there was no protection and almost full flap assymetry could occur. In any model extention of flap in small increments in flight will help early detection before it becomes a major control problem.