Creating an LED array light box
You might find, that at 20mA, the LED forward voltage is slightly less than 3V and will increase the current a bit so go for a slightly higher value resistor with 3 LEDs. 

Upscaling to several strings of LEDs should not be a problem.

You can't put 4 in series because there is nothing to limit the current thru them and, if all four were dropping 2.9V at 20mA, you'd be applying 12V across something that expects 11.6V and this may take a lot more current than 20mA.