The fan switch is an electrical switch, the temp dial is a resistor, and the knob to switch modes is cable.
On the AC not working, I would say that there is only a problem if in fact the ac compressor really "needs" to run to obtain the correct output. So, if it kind of a cool morning, lets say 50 degrees, and you are calling for cabin temp in the "white" zone (70 degrees or so) then it may be appropriate for the ac compressor to not engage. If on the other hand it is a hot day (80 degrees lets say) and the inside temp dial is set all the way to the minimum temp, then I'd expect the ac compressor to come on fairly quickly.

Gilly