sighn up form is not working properly

[listysite76]

my website URL=lislia.com
please help to correct error's of my sighn up form

blow is register.php

include 'config.php';

   
$firstname = $_POST['name'];
$lastname = $_POST['name'];
$email = $_POST['email'];    
$password =($_POST['password']);

//  username already exists

$checkuser = mysql_query("SELECT email FROM users WHERE email='$email'"); 

$username_exist = mysql_num_rows($checkuser);

if($username_exist > 0){
    echo "I'm sorry but the e-mail you specified has already been taken. ";
    unset($email);
    include 'index.html';
    exit();
} 

// lf no errors present with the username
// use a query to insert the data into the database.

$query = "INSERT INTO users (firstname,lastname, email, password)
VALUES('$firstname', '$lastname','$email','$password')";
mysql_query($query) or die(mysql_error());
mysql_close();

echo "You have successfully Registered";
    
// mail user their information

$yoursite = ‘www.blahblah.com’;
$webmaster = ‘yourname’;
$youremail = ‘youremail’;
    
$subject = "You have successfully registered at $yoursite...";
$message = "Dear $name, you are now registered at our web site.  
    To login, simply go to our web page and enter in the following details in the login form:
    e-mail: $email
    Password: $password
    
    Please print this information out and store it for future reference.
    
    Thanks,
    $webmaster";
    
mail($email, $subject, $message, "From: $yoursite <$youremail>\nX-Mailer:PHP/" . phpversion());
    
echo "Your information has been mailed to your email address."; 

[Salvatos]

What is the issue?