What about the indoor fan question.
We need to determine whether the thermostat is doing it's job and sending the 24 volts out to Y1. It will also send 24 volts to G which brings on the indoor fan. If the indoor fan is turning on automatically then the T Stat is probably OK.
If you can see where the LPS, HPS and DT wires plug into the board you can pull the wires off and Ohm out the wires.
LPS= low pressure switch, compressor will not run do to low pressure in refrigerant system.
HPS=high pressure switch, compressor will not run do to high pressure in refrigerant system.
DT =defrost t-stat, I a not am heat pump guy but this probably shuts the compressor of if the coil starts to freeze up.
Any of them could go bad and keep the system from running. Do this with the power off to the unit