Form redirection on configuration PHP page - php

Question

I have a completely functional Form that sends mail as it should and all BUT for some reason, when I (try to) submit my message, instead of showing the success or error alert under the form, it opens the sendmail.php page with the messages, without any CSS... It's been 4 days and I'm going crazy. I'm sure it's actually a stupid typo or something but I can't find it, please help.
Screen of the "Success/Alert" display
Here's my sendmail.php:
<?php
$sendto = 'my#email.com';
$subject = 'Message de votre site';
$errormessage = 'Ah, vous avez oublié quelques informations. Réessayez ? ';
$thanks = "Merci pour votre message ! On vous répond aussi vite que possible. ";
$honeypot = "Vous êtes tombé dans le piège ! Si vous êtes humain.e, recommencez ! ";
$emptyname = 'Quel est votre nom ? ';
$emptyemail = 'Quelle est votre adresse mail ? ';
$emptymessage = 'Et votre message ? ';
$alertname = 'Utilisez uniquement un alphabet standard. ';
$alertemail = 'Entrez ce format de mail : <i>name#example.com</i>. ';
$alertmessage = "Vérifiez que vous n 'avez utilisé aucun caractère spécial. ";
$alert = '';
$pass = 0;
function clean_var($variable) {
$variable = strip_tags(stripslashes(trim(rtrim($variable))));
return $variable;
}
if ( empty($_REQUEST['last']) ) {
if ( empty($_REQUEST['name']) ) {
$pass = 1;
$alert .= "<li>" . $emptyname . "</li>";
$alert .= "<script>jQuery(\"#name\").addClass(\"error\");</script>";
} elseif ( preg_match( "/[][{}()*+?.\\^$|]/", $_REQUEST['name'] ) ) {
$pass = 1;
$alert .= "<li>" . $alertname . "</li>";
}
if ( empty($_REQUEST['email']) ) {
$pass = 1;
$alert .= "<li>" . $emptyemail . "</li>";
$alert .= "<script>jQuery(\"#email\").addClass(\"error\");</script>";
} elseif ( !preg_match("/^[_a-z0-9-]+(\.[_a-z0-9-]+)*#[a-z0-9-]+(\.[a-z0-9-]+)*(\.[a-z]{2,3})$/", $_REQUEST['email']) ) {
$pass = 1;
$alert .= "<li>" . $alertemail . "</li>";
}
if ( empty($_REQUEST['message']) ) {
$pass = 1;
$alert .= "<li>" . $emptymessage . "</li>";
$alert .= "<script>jQuery(\"#message\").addClass(\"error\");</script>";
} elseif ( preg_match( "/[][{}()*+?\\^$|]/", $_REQUEST['message'] ) ) {
$pass = 1;
$alert .= "<li>" . $alertmessage . "</li>";
}
if ( $pass==1 ) {
echo "<script>$(\".result\").toggle();$(\".result\").toggle().hide(\"fast\").show(\"fast\"); </script>";
echo "<script>$(\".result .alert\").addClass('alert-danger').removeClass('alert-success'); </script>";
echo $errormessage;
echo $alert;
} elseif (isset($_REQUEST['message'])) {
$message = "From: " . clean_var($_REQUEST['name']) . "\n";
$message .= "Email: " . clean_var($_REQUEST['email']) . "\n";
$message .= "Message: \n" . clean_var($_REQUEST['message']);
$header = 'From:'. clean_var($_REQUEST['email']);
mail($sendto, $subject, $message, $header);
echo "<script>$(\".result\").toggle();$(\".result\").toggle().hide(\"fast\").show(\"fast\");$('#contactForm')[0].reset();</script>";
echo "<script>$(\".result .alert\").addClass('alert-success').removeClass('alert-danger'); </script>";
echo $thanks;
echo "<script>jQuery(\"#name\").removeClass(\"error\");jQuery(\"#email\").removeClass(\"error\");jQuery(\"#message\").removeClass(\"error\");</script>";
echo "<script>$(\".result .alert\").delay(4000).hide(\"fast\");</script>";
die();
echo "<br/><br/>" . $message;
}
} else {
echo "<script>$(\".result\").toggle();$(\".result\").toggle().hide(\"fast\").show(\"fast\");</script>";
echo $honeypot;
}
?>
And HTML:
<form class="form-inline flowuplabels" role="form" method="post" autocomplete="off" id="contactForm" action="js/sendmail.php">
<div class="form-group fl_wrap">
<label class="fl_label" for="name">Nom :</label>
<input type="text" name="name" value="" id="name" class="form-control fl_input" required>
</div>
<div class="form-group fl_wrap">
<label class="fl_label" for="email">Email :</label>
<input type="text" name="email" value="" id="email" class="form-control fl_input" required>
</div>
<span class="form-group fl_wrap honeypot">
<label class="fl_label" for="last">Honeypot:</label>
<input type="text" name="last" value="" id="last" class="form-control fl_input">
</span>
<div class="form-group fl_wrap">
<label class="fl_label" for="message">Message :</label>
<textarea type="text" name="message" value="" id="message" class="materialize-textarea" required></textarea>
</div>
<div class="form-group">
<button type="submit" value="Send" id="submit" class="btn btn-block">Envoyer</button>
</div>
<div id="form-alert" class="form-group">
<div class="result">
<div class="alert"></div>
</div>
</div>
</form>
As some asked. The HTML is on the index page and the sendmail.php is an independent page.
And this is where the success/alert message is supposed to appear :
Form in website