501x

I had installed a 96-98 kicker Impulse into my car, its in a enclosed box btw. Well Im running a 501x amp which I bridged two channels on the rear to it. Thats all thats running on the amp, since I havent bought front speakers yet to run it to, Im leaving the back speakers stock. Anyway, I find that when I put it on HP, it gives more bass than if I put it on LP, Why is that, and will that ruin the amp? My amp started shutting off if my bass got too high, and I had to lower the volume for a bit for the woofer to hit again. It killed my battery in the long run, but I was told It wasnt enough power to have a cap on.

Something wrong with the crossover in the amp, maybe?  You shouldn't have more bass on full range than you would at low pass.  In this case, playing all frequencies may make it just seem to be more bass.  Something else wrong with the impedance with that setup.  The amp cutting off means there is a problem with the impedance load the sub is giving it.  Or the amp gain is set incorrectly.

Start back with the basics:  make sure the ohm load of the sub is no less than 4 to bridge it to the amp.  Check ground connection and test it.  Adjust the amp gain to the voltage input from the head unit.  Make sure power wire is large enough for the amperage the amp is pulling.

And make sure you don't have any crossovers engaged at the deck that would affect the sub.