If you have issues relating to engine noise (ie RPM) then you have a bad earth somewhere, 100%

Did you use all new cables??
Did you solder and wrap all joins with electrical tape?
Did you run any wires through a hinged area of the car? (ie folding rear seats)
Is the head unit/amp earthed to a part of the chassis and not some random earth you found behind where the head unit sits? If this is the case, and I would suggest it is even without seeing it, PLEASE re-run an earth and solder it, or at the very least pinch the end of the wire under an unpainted bolt/screw you find behind the head unit or around the front seats.

It really sounds to me like you've got the earth (-ve) of the head unit/amp connected to the earth running from the ignition barrel or a dirty connection. If this turns out to be good then somewhere along the line you've got a bad earth from one of the cables you've run.

Also make sure you're +ve and -ve power cables are of the same diameter from and to the amp

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