Question About Cache

Your code is working perfectly, the problem is that you can not set external cache files, in case the links that do not have a good cache usage are these:

https://i.ytimg.com/vi/iSxbI3d0064/hqdefault.jpg (5 minutes)
https://i.ytimg.com/vi/-IZc6i5K2OQ/hqdefault.jpg (2 hours)
https://i.ytimg.com/vi/3t9O5DpRfxU/hqdefault.jpg (2 hours)
https://i.ytimg.com/vi/4KDQ0IjMsnA/hqdefault.jpg (2 hours)
https://i.ytimg.com/vi/4QTwsLTv4Kc/hqdefault.jpg (2 hours)
https://i.ytimg.com/vi/4Uw8EcNmLC4/hqdefault.jpg (2 hours)
https://i.ytimg.com/vi/4cLtiYvRvfE/hqdefault.jpg (2 hours)
https://i.ytimg.com/vi/ALM1CwRMrmw/hqdefault.jpg (2 hours)
https://i.ytimg.com/vi/AQ0resnXCcE/hqdefault.jpg (2 hours)
https://i.ytimg.com/vi/Br-mOQ_x-Ik/hqdefault.jpg (2 hours)
https://i.ytimg.com/vi/EU1SaAun2r0/hqdefault.jpg (2 hours)
https://i.ytimg.com/vi/EoYOCxP6yIA/hqdefault.jpg (2 hours)
https://i.ytimg.com/vi/F2vea_JoBaw/hqdefault.jpg (2 hours)
https://i.ytimg.com/vi/TCZpKB7l8-Y/hqdefault.jpg (2 hours)
https://i.ytimg.com/vi/U1aXAYjgy5w/hqdefault.jpg (2 hours)
https://i.ytimg.com/vi/ULwcsIPdc8w/hqdefault.jpg (2 hours)
https://i.ytimg.com/vi/W_sFQN8RL1E/hqdefault.jpg (2 hours)
https://i.ytimg.com/vi/WuCGE6Sl27w/hqdefault.jpg (2 hours)
https://i.ytimg.com/vi/Y-D7PHnn70k/hqdefault.jpg (2 hours)
https://i.ytimg.com/vi/byZO3dMLtpA/hqdefault.jpg (2 hours)
https://i.ytimg.com/vi/clRjbYa4UWQ/hqdefault.jpg (2 hours)
https://i.ytimg.com/vi/eBZjZ6eAzMw/hqdefault.jpg (2 hours)
https://i.ytimg.com/vi/iQpGq4HguVs/hqdefault.jpg (2 hours)
https://i.ytimg.com/vi/lSLwVPih4_w/hqdefault.jpg (2 hours)
https://i.ytimg.com/vi/m1ssAFzaCsU/hqdefault.jpg (2 hours)
https://i.ytimg.com/vi/qLKGcB4uE-g/hqdefault.jpg (2 hours)
https://i.ytimg.com/vi/rTisfEc786c/hqdefault.jpg (2 hours)
https://i.ytimg.com/vi/rhUvo4xj2oU/hqdefault.jpg (2 hours)
https://i.ytimg.com/vi/wdvI62lq78I/hqdefault.jpg (2 hours)
https://i.ytimg.com/vi/wkGH7W8WPYU/hqdefault.jpg (2 hours)
https://www.google-analytics.com/analytics.js (2 hours)

No one belongs to your domain, Google encourages several good practices, but their own tools (google analytics and youtube) rarely follow this.

Achieving 100/100 in PageSpeed Insights does not mean that your site is great for the end user, your page for example uses the <style> tag at a time when it could be inside and a .CSS that would take advantage of the cache and has a <script> tag with a function called function tocar(id) , could be within a .JS .

There are several links on your share page that could be automated through jQuery (which you already use) or even Javascript purely, rather than doing so:

<p class="center no"><a href="https://www.facebook.com/sharer/sharer.php?app_id=1731086990510840&u=http://procurar.netescola.info/baixar/iSxbI3d0064&display=popup&ref=plugin&src=share_button" class="fb" target="_blank" title="Compartilhar Música no Facebook"><i class="fa fa-facebook" aria-hidden="true"></i><br>Compartilhar</a></p>

It could be something like:

<p class="center no"><a href="javascript:void(0);" data-video-id="iSxbI3d0064" class="fb" title="Compartilhar Música no Facebook"><i class="fa fa-facebook" aria-hidden="true"></i><br>Compartilhar</a></p>

And in jQuery something like:

$(document).on("click", ".fb", function() {
    var url = 'https://www.facebook.com/sharer/sharer.php?app_id=1731086990510840&u=http://procurar.netescola.info/baixar/' +
               $(this).data("video-id") +
              '&display=popup&ref=plugin&src=share_button';

    window.open(url, "_blank");
}, false);

But they are just suggestions and there are several ways to solve this.

Now to solve the problem of external requests you could try to solve this is by using a "proxy" in a programming language, I do not recommend applying to everything, only in youtube thumbnail images.

Create a file called thumb.php:

<?php
$time = 365 * 24 * 60 * 60; //Defina o tempo de cache aqui, por padrão deixei o cache de 365 dias
$cacheThumbPath = 'thumbcache/'; //Defina a sua pasta de cache aqui (mantenha a / no final)

$http_version = empty($_SERVER['SERVER_PROTOCOL']) ? 'HTTP/1.0' : $_SERVER['SERVER_PROTOCOL'];

if (empty($_GET['id']) || !preg_match('/^[A-Za-z0-9_\-]{11}$/', $_GET['id'])) {
    header($http_version . '400 Bad Request', true, 400);
    echo 'ID não definida na url';
    exit;
}

$id = $_GET['id'];
$cacheThumbPath .= $id . '.jpg';

function cachePage()
{
    global $http_version, $time;

    header('Content-Type: image/jpeg');
    header('Expires: ' . gmdate('D, d M Y H:i:s', time() + $time) . ' GMT');
    header('Cache-Control: public, max-age=' . $time);
    header('Pragma: max-age=' . $time);
}

//Verifica se já existe uma cópia do arquivo no seu servidor para evitar requisitar várias vezes o youtube
if (file_exists($cacheThumbPath)) {
    cachePage();
    echo file_get_contents($cacheThumbPath);
    exit;
}

$ch = curl_init();

$thumburl = 'https://i.ytimg.com/vi/' . $id . '/hqdefault.jpg';

curl_setopt($ch, CURLOPT_URL, $thumburl);
curl_setopt($ch, CURLOPT_RETURNTRANSFER, true);
curl_setopt($ch, CURLOPT_BINARYTRANSFER, true);
curl_setopt($ch, CURLOPT_SSL_VERIFYPEER, false);
curl_setopt($ch, CURLOPT_TIMEOUT, 5);

$data = curl_exec($ch) or die(curl_error($ch));

curl_close($ch);

//Salva cópia do arquivo no seu servidor
if (file_put_contents($cacheThumbPath, $data)) {
    cachePage();
    echo $data;
    exit;
}

header($http_version . ' 500 Internal Server Error', true, 500);
echo 'Erro ao baixar ou ler a imagem, detalhes:';
print_r(error_get_last());

And in HTML call it like this:

<div class="capayt" style="height:350px; background:url('http://netescola.info/thumb.php?id=m1ssAFzaCsU');" alt="Hardwell Live at Ultra Music Festival Miami 2016 - Procurar Musicas"></div>