Why does the outside fan stop but the blower fan continues to run?
I think the outdoor unit fan turning off while the AC is still running is normal - I know that happens quite often in my own home (and my previous home), and the AC has always worked fine.

As for the temperature, how new is your thermostat?  In my current house, I have a thermostat from about 30 years ago (one of those dial-style thermostats), and while it works fine in general, the temperature it's set to has very little relation to the actual temperature in the house.  If it's cold, we turn the thermostat up a little, and vice versa, and it works out fine.