you also need to consider the sub and what its power handling capabilities are as well as what type of box you are going to use as that will directly affect the subs power handling capability
if the stereo is the amplification for the mids and highs, i would agree with grounding your rca to the stereo chasis to see if the noise goes away, if the noise goes away when you unplug the rcas then it is likely the rcas or the amp has an issue
the protection circuit on the amp is usually triggered by a low resistance load on the amp, could also be a voltage supply issue ie. bad ground, bad fuse, or bad connection somewhere in the power or ground path, hope this helps
there is a physics law that states that if any 1 single device in a circuit draws more than 20% of the total output of the source then damage will incur to the source. so really you need to take the rated amperage of your alternator and determine what 20% would be. then any amp that does not...