Yes, the 15 sure could over power your door speakers but you don't have to turn your gain to maximum. Another set of 6.5's for the rear could be done, and you power them with the head unit. Or, could even leave the pyle's in the rear, since you'd have things faded towards the front of the car which will hide their craptastic-ness and still provide some rear fill if you like. This is a personal preference thing, 80% of the sound coming from the front/20 from the rear sounds pretty natural to me. Some people (tall) sit with their heads in the back seats and hate it. I personally don't have rear speakers fwiw.

In a budget build you want to get the most out of your equipment so-

Here is the 12in version with enclosure.

For door treatment, the cheap and dirty way... and the obsessive professional way... watching those two should get you going there.

Bridging the amp will be detailed in the amp manual, but essentially yes. Two channels are wired as one for the sub with the subwoofer voice coils in series for a 4 ohm load, in this case.