The RGB connections are just backlights... It won't change the colour of the text... However, the appearance may look like a change of colour...
Just connect a transistor to each of the pins.. Connect the base of the transistor via a suitable resistor to the pin of the micro... Also connect the collector via the recomended resistor to the RGB connections on the display... The emitter to ground.
As for the contrast... I have never connected that through PWM.... I'm not even sure its the best way to go... I would personally use a digital pot for that...