This can go a couple of different ways, but my suggestion for just ease of the install is to leave the OEM wiring where it's at and just connect your speakers straight to the OEM wiring. Then run your speaker wire from the harness to your amp. Connect the RCA's, set your gain and voila. (For a tip on setting your gain you can check here...
Rockford T212D2 too much for 370z?
Also, yes you would run your door/dash in parallel.