As I understand it (and I'm not absolutely sure) the caps in the thing are to aid the motor in starting. If they were shot, the compressor might have more trouble starting up. this could draw more current - once it actually does get running, they don't do much of anything. If they were shorted, you'd pop the breaker. If they were open, the motor might have trouble starting.
A heat pump has a valve that gets switched to change the things function from heating to cooling (i.e., it reverses the operation). This is probably controlled by a solinoid valve. That might be what you are hearing. Depending on the type, it may need to be energized for cooling, and when 'released', switch to heating, or it could run the opposite way (these have a spring to return it to the 'rest' state when deenergized). Some get moved to one position, then the power is removed. To move it the other way, it reverses the polarity, and the thing goes back the other way. These do not have power applied all the time. If this was sticky, I don't think it would double the power, unless it ended up in the middle...then the unit might 'run', but not be doing much for that time.
Unless the unit is running nearly twice as long, on most, if it has the proper CB, it would normally pop the breaker, as the CB is not normally twice as big as the normal load.
Most a/c units also have a heater in them to ensure it doesn't have moisture that could end up frozen. This might humm, but normally doesn't.
Someone who has more intimate knowledge can probably give you some other thoughts.