Technically, it's working at it's maximum *capacity* at all times, efficiency is a function of the temperature difference between the high-pressure and low-pressure heat exchangers (more temperature difference, more efficiency of the gas cycle).

Your 3rd issue is basically the same as the 2nd issue -- the AC can't keep up because the insulation is so bad. But most modern houses with a well-maintained AC unit should be able to keep up with mid-90's for ambient temperature, even with a high wet bulb (dew point) temperature.