Subwoofer issue

Check your crossover settings. If they are good, sounds like a bad hesd unit or connections...

When you sap "pop",do you mean a loud crackle/static noise,or do you mean that the 5x7 and sub are thumping so hard to the bass that the speaker cone is hitting hard against the magnet? What type of amp and what is the power rating? It sounds like you have the amp connected to the line level output from the right rear speaker.Which would also say why both that speaker and the sub are creating this problem.When the engine is running,the ammount of power available to both the sub and 5x7's increases due to the alternators additional output.So keeping the vol set at the same level would be much louder when engine is running.There's a chance that you have the line level output from that one speaker connected to a standard low impedence RCA jack.The extra power from the head unit could be overloading the amp's input.

The other problem could be that you are simply over-peaking your amps peak output.This temporarily overloads the amp and causes it to "click" and turn off then back on.This is normal and is there to prevent you from toasting your amps internal circuitry.

Another problem could be that some high or low frequency noise is being induced within that channel.You could have a ground loop going on here.If this is the case,one of the things you could try is relocate the amps ground wiring or get a ground loop isolator.

Make sure all of your connections are well secured.Don't loop wiring around other wires.Try to keep your components power wire (positive) well separated from any input signal wire (eg.. the RCA input on your amp).And as with all subwoofers,make sure you are using a crossover,specifically a low-pass x-over.Without a x-over,your wasting valuable power on frequencies your not supposed to be hearing from a sub.