That MOSFET is a winner device for allowing the Arduino to control lots of high power devices. Just be sure to heat sink the MOSFET if passing more then just a couple of amps. Turns out the the heat dissipation rating tends to be the limiting factor, rather then volts or amps rating, in keeping the device in it's SOA, safe operating area.
Actually a series resistor is not required between the Arduino output pin and the MOSFET gate and a higher ohm series resistor will act to actually slow down the turn-on and turn-off times as the MOSTFET gate acts like a capacitor and should be driven with as much current drive as possible during the switching transitions. The key to these power MOSFET devices is to insure they switch on and off quickly as the more time spend in the transition region adds significantly to the heat dissipation problem.
Once the MOSFET is fully on or off the gate draws no DC current at all. That aside it's always a good practice to have a smallish series resistor on all Arduion I/O pins but for other reasons, and a 330 ohm series resistor is more then enough to protect an output pin. A 1K or 2K resistor is a good value for a series protection diode for an input pin.
No series protection diode is needed for the output pin and in fact would interfere with the proper turning on or off of the MOSFET gate. What you might consider as a safety precaution is to wire a pull down resistor at the MOSFET gate to ground, say 2K ohms or so. If the arduino was to be powered off, but the 12vdc was still on there is a tendency for the gate of the MOSTFET to 'float' and cause the device to turn on slightly, but a pull down resistor will insure it remains off if gate drive signal is lost.
As far as the a diode connected in reverse bias across a load, it is not be needed for driving a resistive load like a heater or large lamp, as they are non-inductive loads. When turning off an inductive load like a motor or a solenoid, the magnetic field collapses and cause a very short reverse voltage spike that can approach X4 negitive the normal applied positive voltage. That is where a diode wired across the inductive load can help by allowing the spike to just circulate between the coil and the diode and dissipate the spike current thus protecting the switching device.
The spike is very short so a 1 amp diode should be able to handle the spike current OK and the 1N400X series is a pretty popular choice in the past, although the newer Schottky diodes have faster switching times and are more often used these days even if they costs more then the 1N400X series diodes.
Note the most power MOSFET have built in protection diodes but it never hurts to have an external diode installed right at the motor or solenoid terminals as it helps limit the electrical noise and spike that can otherwise radiate and bounce the power and ground wiring.