PHP, MySQL Insert Into table in localhost

Using PDO is a better approach:

function validatePost($post) {
    return (isset($post['name']) &&
        isset($post['email']) &&
        isset($post['place']) &&
        isset($post['level']));
}

function createTable(PDO $pdo, $name, $query) {
    if (tableExists($pdo, $name)) {
        throw new Exception("Table already exists");
    }
    $pdo->query("CREATE TABLE $name($query)");
}

function tableExists(PDO $pdo, $name) {
    $result = $pdo->query("SHOW TABLES LIKE $name");
    return count($result->fetchAll());
}

$dbhost = 'localhost';
$dbname = 'applicants';
$dbuser = 'root';
$dbpass = 'root';

validatePost($_POST);
try {
    $pdo = new PDO("mysql:host=$dbhost;dbname=$dbname", $dbuser, $dbpass);
    $pdo->setAttribute(PDO::ATTR_ERRMODE, PDO::ERRMODE_EXCEPTION);
    createTable($pdo, "customers",
        "name VARCHAR(16),
         email VARCHAR(16),
         place VARCHAR(16),
         level VARCHAR(16)");

    $stmt = $pdo->prepare("INSERT INTO `customers` (`name`, `email`, `place`, `level`) VALUES(:name, :email, :place, :level)");
    $stmt->bindParam(":name", $_POST["name"]);
    $stmt->bindParam(":email", $_POST["email"]);
    $stmt->bindParam(":place", $_POST["place"]);
    $stmt->bindParam(":level", $_POST["level"]);
    $stmt->execute();
}
catch (PDOException $e) {
    echo "There was an error regarding the Database: " . $e->getMessage();
    die();
}
catch (Exception $e) {
    echo "Error! " . $e->getMessage();
}

You have a PDO object which acts as the connection, it is then passed around the functions in order to operate.

Points

• PDO supports prepared statements, which removes the need to sanitize (the prepared statement does it for you!)
• When inserting, it's considered a good practice to expicitely declare which column gets what, I've assumed the names of your columns, but you should change them if they don't match.
• Don't echo, throw Exceptions. Throwing an exception allows you to deal with problems and errors in your code much more efficiently and easily. You throw an exception and catch it where it may occur. An uncaught (catched) exception will terminate the script.

In index.php, the query should be

mysql_query($query)

not queryMysql.

Plus, make sure you are inserting every field in the database. If you have auto increment field or field which you aren't using, use this syntax

INSERT INTO products (column 1, column 2) VALUES (value1, value2) 

p.s. Change your all queryMysql to mysql_query(). I believe there's no function like queryMysql (i have stopped using this mysql_* functions long ago so i could be wrong but about mysql_query() i am sure that it'l work).