Driving a fan using a mosfet, do I need a diode?
1) Depends on the fan, if it has inductance (A DC brushed motor) then you may want some kind of over voltage protection like D1. If its a brushless DC motor (like a PC fan) then it already has a circuit built in for overvoltage protection or it doesn't need it. 

2) It says 500mA right in the datasheet, your fan can't be more than this. A 320mA fan will be fine. The mosfet also has a 5Ω RdsOn which means its like a 5Ω resistor when its on. At 320mV this will cause the voltage of the fan to be 1.6V, a fan with a controller may or may not be able to tolerate this.