My answers, please read the readme.md for my explanations

answer1.php

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

answer3.php

$input = array(1,22,9,0);
var_dump(nextFibonacci($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); 
}