Why two resistors at Gate side of IGBT
R5 controls the gate current (and possibly prevents damaging current from flowing back to the driving circuit if there is some source inductance). It slows the turn-on, and the diode shunts it so the IGBT turns off quickly. 

R9 (gate to emitter) is just there to keep the IGBT 'off' if the driver gets disconnected, removed from the socket, or goes high impedance. Without that, you could get shoot-through under that condition which would destroy the IGBTs- since they're in series across the supply voltage. A 0.1 cent resistor is cheap insurance.