1. Since I'm using existing motor control circuit from my car I don't need any resistor to attach to the microcontroller pin. I can directly attach soldered wires to MC pins. Is this correct?
That depends on whether these resistors go to some kind of driver or directly to the motors, but I'd guess the former.
What are the values of the resistors?
What do they connect to?
What do you have to do/connect to make the motors move as it is?
If you have a multimeter, measure the resistors (if you haven't, do get a cheap meter ASAP, as it's hard to make any kind of electronics without a multimeter). If not, tell us the color bands/rings on the resistors.
2. Do I need to connect VSS from my microcontroller to the -ve of my car power source? If not, what/how exactly do I need to connect power source from car and controller board?
You need to connect Vss of the controller to the ground (0V) of the cars circuit. The reason I don't write the "-ve", is that I don't know whether your car has got some sort of a split supply, in which case "-ve" could be less than 0V/ground (although it's not very likely with a 3-cell battery).
If they're not interconnected, the signals will have no reference and will thus not control anything.