AVR and MOSFET gate resistor
No you do not need a series resistor. If you put one in there it would limit the current a bit and might help in case of some layout issue, but it's not necessary. 

Why the rather low gate pull down and why a pull down rather than pullup? Normally I'd expect to see more like a 20K pullup so if the AVR output is high impedance the motor turns off. A pull down resistor on a P-channel MOSFET gate means that the motor will turn on if the input is open.