The reason to unfeather the prop after starting the first engine according to me is not the extra electrical power you get for starting the second engine but to help in charging your battery before starting your second engine.
It indeed states in the AFM:
"When battery starting, unfeather propellor of first engine and delay start of second engine for 30 secs to allow completion of flight guidance computer start-up self-test."
But in my book it also states to: "delay an engine start until the main battery load is below +.50."
So to get the battery load below .50 engage your AC generator by unfeathering your propeller.
About push back with both engines unfeathered.
We used to do that but not anymore. The reason is that if your P/L is not at or aft of disk your nose gear will be subjected to undue stresses.