Connect optocoupler 4N35 to Arduino Uno to control LED light strips
Can i connect the optocoupler's emmitter to the arduino ground?


Yes. Don't forget to either enable the internal pullup on the GPIO pin or use an external pullup on the collector.


  If i power the arduino with 12 V D.C power source connected to the D.C jack, can i give the power to the LEDs also using the V-in pin of the arduino?


Not at the current rating you are talking about, no. The header is only rated for 1A, and the diode on the barrel jack input is also rated for only 1A.  You would need to split the LED power off from the incoming power before it goes into the Arduino.

The way you have your MOSFETs wired at the moment is wrong. The moment you turn one on it will let the Magic Smoke escape. You are using them to short circuit the LEDs, which is very very bad.

Each one should be wired in series with the LED between the cathode and ground:







simulate this circuit &ndash; Schematic created using CircuitLab