My answers [1-4]

answer1.php

<?php /*
Explanation
This is very simple i just compare the two arrays if the second array is in first array i make it to show true 
*/
function isSubset($array1, $array2) {
    echo (!array_diff($array2, $array1) ? "true" : "false");
}

//output
isSubset(array("A","B","C","D","E"), array("A","E","D")); // true
isSubset(array("A","B","C","D","E"), array("A","D","Z")); // false
isSubset(array("A","D","E"), array("A","A","D","E")); // true
?>

answer2.md

//I have no knowledge about cache yet :(

answer3.php

<?php
/*
Explanation
Firts i need to determine the number of input array is the perfect root or not so i have create the isPerfectSquare($n) function.
n is Fibinacci if one of  5*n*n + 4 or 5*n*n - 4 or both is a perferct square so the isFibonacci($n) function return 1, if its match.
Next, i created a function to determine the upcoming fibonacci number. 
i loop reversly from given number to 0, and i brake the loop if any number is fibonacci, i stored that value and divide by fibonacci ratio.
*/

$input = array(1,22,9,0);
var_dump(nextFibonacci($input)); //output [2,34,13,1]

function nextFibonacci($input) {
    foreach($input as $i) {
        while($i>=0) {
            $store[] = $i;
            if(isFibonacci($i)) 
            break;
            $i--;
        }
        $last = end($store);
        if($last == 0) {
            $output[] = 1;
        } else {
            $output[] = round($last/0.618);
        }
    }
    return $output;
}

//Checking for square root
function isPerfectSquare($x) 
{ 
    $s = (int)(sqrt($x)); 
    return ($s * $s == $x); 
}

//Determining the fibonacci number
function isFibonacci($n) 
{ 
  return isPerfectSquare(5 * $n * $n + 4) || isPerfectSquare(5 * $n * $n - 4); 
}

?>

answer4.js

//Problem is var i = 0; is not a global scope. so i have changed the var to let.
function createArrayOfFunctions(y) {
  var arr = [];
  for (let i = 0; i < y; i++) {
    arr[i] = function(x) {
      return x + i;
    }  
  }  
  return arr;
}