The RGB strips already have the resistors in line with each series of LEDs so there is no need to add any more to limit the LED current.
However, you do need a resistor of 100 ohms or so in line with the gate of the FET to protect the arduino's output.
The TNtqi.png drawing shows just an RGB LED and these DO need a series resistor in each cathode of the LED. Driving just the one LED from 12V is a bit of a waste, you might as well drop this to to 5V. You can't connect common anode RGB LEDs in series to make use of the 12V. On the RGB strip each colour of LED is a separate with access to both anode and cathode, allowing them to connect in series and have one resistor for every three LEDs.