Automatically link youtube videos

You could try with a php function the following:

<?php
function getYouTubeVideosByTag($tag, $maxResults = 6) {
    $apiKey = '[your youtube API key]';
    $channelId = '[your-youtube-channel-ID';

    // Forza formato hashtag
    $query = urlencode('#' . $tag);

    $url = "https://www.googleapis.com/youtube/v3/search?part=snippet&type=video&order=date&maxResults=$maxResults&q=$query&channelId=$channelId&key=$apiKey";

    $response = file_get_contents($url);

    if ($response === FALSE) {
        return [];
    }

    $data = json_decode($response, true);

    $videos = [];

    if (!empty($data['items'])) {
        foreach ($data['items'] as $item) {
            if (!isset($item['id']['videoId'])) continue;

            $videos[] = [
                'title' => $item['snippet']['title'],
                'videoId' => $item['id']['videoId'],
                'description' => $item['snippet']['description'],
                // 'thumbnail' => $item['snippet']['thumbnails']['medium']['url']
            ];
        }
    }

    return $videos;
}
?>

Obviously you have to link this function in every web page you want links your videos, and in these pages you can call that function by a code like this:

<?php
if (!empty($youtubetag)) {

    if (is_array($youtubetag)) {
        $query = implode(' OR ', array_map(fn($t) => '#' . $t, $youtubetag));
        $videos = getYouTubeVideos($query, 5);
    } else {
        $videos = getYouTubeVideosByTag($youtubetag, 3);
    }

    if (!empty($videos)) {
        ?>

        <section class="youtube-videos">
        <h2>🎙️ Our podcast (YouTube)</h2>

            <ul>
                <?php foreach ($videos as $video): ?>
                    <li class="podcast">🎙️
                        <a href="https://www.youtube.com/watch?v=<?= $video['videoId'] ?>"><strong><?= htmlspecialchars($video['title']) ?></strong></a>:
                       <?= htmlspecialchars(substr($video['description'], 0, 120), ENT_QUOTES | ENT_HTML5, 'UTF-8', false) ?>
                    </li>
                <?php endforeach; ?>
            </ul>
        </section>

        <?php
    }
}
?>

Finally, you should define, possibly in the head of each php page, where you want to link youtube videos, the variable $youtubetag:

$youtubetag="my tag";
or 
$youtubetag="['mytag1', 'mytag2']";

Connecting a wordpress category to a facebook page

IFTT is a good app, but with a free plan you can connect only one wordpress category to one facebook page.

There are many plugins and many web services, such as Zapier, or Activepieces, that can connect wordpress with a facebook page, but if you have a free wordpress plan (with an address like yourdomain.wordpress.com) you can install plugins only upgrading your plan.