How to protect a P-channel MOSFET when driving a motor?
Your basic concept makes sense, but you missed the fact that the "12 V" line of a car will sometimes have significant voltage spikes on it.  Any cicuit connected directly to this power needs to be able to withstand 50 at least for short periods.

When the pump is on, even a short spike will apply high voltage to the FET gate, which will blow out the oxide instantly.  Overvoltaging the FET S-D isn't good either.

Use a 60 V FET, and do something to clamp the gate voltage to a safe level.

Added:

I forgot to mention this earlier since the main issue was about nasty voltage spikes on the vehicle power line.  No, 1N4007 is a bad choice for the diodes.  In this case, I'd use Schottkys rated for 20 or 30 V.  Those are cheap and readily available.  Since the current will only run in them for a short time as the stored inductive energy is dissipated, you can use the peak current rating instead of the continuous current rating of the diodes.  The diodes need to be able to handle peak current of whatever the motor current is.