Why is D3 wired to be forward biased when the relay is ON? This would shunt the current thru D3 rather than solenoid valve, right?
Yes D3 is clearly backwards. That's easily fixed though.
should I use a MOSFET or relay as a switch to turn on my pump it is a 12V 3A water pump.
Either can be used, but which is better suited, depends on the application.
A relay is more electrical robust, in that it won't be destroyed by moderate over-voltage and high current surges, but has a limited mechanical life. Frequency switching will cause rapid deterioration of the contacts.
A MOSFET, has no limit to the number or switching cycles, but is much more sensitive to electrical damage from electrostatic discharge and over-current.