AC not shutting of automatically
If the evaporator will ice up depends on the type of control if it is orifice or capillary tube control it may Ice up but if a thermal expansion valve called TXV this regulates the flow and it should not but I have seen TXV controlled system ice up a few times.
As far as your system not shutting off when the temp is reached this is to keep the system from short cycling there is a setting sometimes called “dead band” usually around 3 degrees and is set in your thermostat it may be a setting like +2 -2 this would be a 4 degree dead band or the thermostat won’t turn the heat on until 2 degrees below set point and won’t shut off until 2 over set point same with the ac, you can usually change these I change mine based on season +0 -2 is my summer setting and +2 -0 is my winter setting. If it takes 10 minutes to change 1 degree a 2 degree dead band is ok but if you reduce it two far your energy cost will go up and the life of your system may be reduced from the repeated startups.