how to implement PWM LED fading into a random case switch?
In order to fade in and fade out LEDs you need to use PWM feature. And, specifically you need to use the analogWrite() function call. Also, you need to make sure all your LEDs are connected to PWM port pins.  Port pins which support the PWM feature for various Arduinos are listed in the above link.

In your code you might try replacing your 500ms delay with a count up followed by a count down loop.  Each loop should contain the appropriate delay and count up or down to the appropriate value.

For instance, you might try a 1ms delay and a count from 0 to 255 followed by a count from 255 to 0.  In both loops just before or just after calling the delay() function, place the call to the analogWrite() function and pass the counter value as the PWM duty cycle (LED brightness setting).

added later...

For example, you might try to see if this code works for the 1st case statement:

int brightness_level;


case 1: //if ledcolor equals 1 then the led on pin 11 will turn on etc.
  for(brightness_level = 0 ; brightness_level &lt; 255 ; brightness_level++)
  {
    analogWrite(11, brightness_level);
    delay(1);
  }
  for(brightness_level = 255 ; brightness_level &gt;= 0 ; brightness_level--)
  {
    analogWrite(11, brightness_level);
    delay(1);
  }
break;