Welcome aboard!
#1, run when water temp is 55 and above, do NOT run in winter, it will super-cool the water in below freezing events, you want the most 39 deg water in the bottom of the pond. Ice over is a good thing when temps get really cold.
An alternative is move diffuser into 3' water when temp drops below 50-55.
#2, stagnation will occur without aeration if conditions are right, if aerating, you won't have that issue.
#3, if you are supplementing water during summer, run it into pond direct, don't atomize it with a sprinkler. 30-40% will be lost to evaporation. the aerator is keeping your water from becoming anoxic. If for fishing, add all types of structure/habitat, deep, shallow and everything in-between.