Loud noise from outdoor unit several seconds after AC turns off
If there is a bad spring in the compressor , the compressor can be replaced, you do not have to replace everything.
  In cooling mode the outside unit should never need a defrost the condensing coils are actually hot, if there is any ice it would normally be on the suction line and is normally caused from a low charge but an over charge can also cause icing. 
As far as the torpedo noise I am not sure what you are describing but if non compressibles (air) has gotten into the system it can sound louder as the high side pressure drops once the compressor stops. With the noise and possible icing it is time to call a tech and make sure your unit has a proper Freon or refrigerant charge. As far as a home warranty if it is covered you should use it but at this point a service call is needed to identify what the problem is. You should get a recording of the noise so the tech can hear it it could be something like the reversing valve opening since you mentioned the temp set back but that is a guess, as It is really the only thing I can think of that would really dump the pressure and make a noise intermittently.