RGB LED Strip - several question from newbie
Yes, But the cathode (negative part) of the diodes in adafruits example is connected to R/G/B. Then, when you apply power to the common anode (positive side), the pin (R, G or B) you pull low to ground will light up. 
Your adapter doesn't just push out 6A; it is able to provide 6A at 12V. You can power any 12V device with it requiring less than 6A. Say you connect 3 diodes in parallell that consumes 20mA each, the output of the adapter will only measure 60mA. 
If the circuit powered by the adapter requires more than 6A, your adapter will start heating up and break. 
Yes, but I guess you have to read up on some basic skills before trying this, i.e be really sure of how the circuit is connected before calculating the size of your resistors. Too low R = broken circuit. Too high R = non functioning circuit.