Une fonction utilisateur qui pose problème.

Bonjour,
Je viens de terminer d'écrire un petit formulaire d'inscription, avec quelques fonctions personnalisées. Cependant, 2 erreurs surviennent lorsque je commence à tester le travail "fini" :

1) Quand je ne remplis pas tous les champs, j'obtiens une erreur indiquant qu'au moins un champ est vide (normal, j'ai défini une constante qui contient ce texte, et la condition du if(...) n'est pas remplie) ;

2) Quand j'essaie de remplir convenablement les champs pour réaliser une "vraie" inscription. Si elle réussit, je veux voir s'afficher un texte (en l'occurrence, 'OK !'), sans envoyer les infos dans une bdd. Le problème : une fonction (que j'ai créé) fait des caprices et ne remplit pas la condition du second if(...).

Pourriez-vous m'aider à corriger ma/mes fonction.s et/ou mon formulaire ?
Merci d'avance :)

fonctions.php

<?php

function secure_password($password)
{
  if(preg_match("#[a-z]#",$password) AND preg_match("#[A-Z]#",$password) AND preg_match("#[0-9]#",$password) AND strlen($password)>7)
  {
    return 1;
  }
  else {
    return 0;
  }
}

function allowed_chars($str)
{
  if(preg_match('#^[a-zA-Z0-9._\[\]\|\$\!@=\+&-]$#',$str)) // Caractères spéciaux autorisés :  ._[]|$!@=+&-
  {
    return 1;
  }
  else
  {
    return 0;
  }
}

function valid_username($username)
{
  if (allowed_chars($username) AND strlen($username)>5 AND strlen($username)<33)
  {
    return 1;
  }
  else
  {
    return 0;
  }
}

constants.php

<?php

define('WEBSITE_NAME','example.com');

// MAILING CONSTANTS
// Change the following constants to correspond to your own website.
// It is particularly important for website with newsletter, confirmation's mail,...
// Be careful with WEBSITE_SENDING_EMAIL (and possibly WEBSITE_EMAIL_SENDER) since some spam filters block addresses that
// does not match with the informations in the 'From: ...' part of the mail's header.

define('WEBSITE_EMAIL_SENDER','no-reply');
define('WEBSITE_SENDING_EMAIL','***@***');
define('WEBSITE_EMAIL_RECEIVER','replying-add');
define('WEBSITE_RECEIVING_EMAIL','***@***');

// ERRORS CONSTANTS
// Change the following constants to correspond to you own functions and errors
// Please, note that each occurences of an error must be modified in each files where it appears if you modify its name.

define('ERR_EMPTY_FIELDS','An error occured: at least one obligatory field is empty. Please, fill all marked fields.');
define('ERR_EMAIL_WRONG_FORMAT','An error occured: the format of the string does not match with the format of an email address.');
define('ERR_EMAIL_NOT_MATCH','An error occured: the email address does not match its confirmation.');
define('ERR_EMAIL_USED','An error occured: the email address is already in use.'); // You can also give a link to restore the user's account.
define('ERR_USERNAME_UNKNOWN','An error occured: the username is not registered.'); // You can also give a link to create an account.
define('ERR_USERNAME_WRONG_FORMAT', 'An error occured: the username is incorrect.');
define('ERR_USERNAME_USED','An error occured: the username is already in use.');
define('ERR_PASSWORD_NOT_MATCH','An error occured: the password does not match its confirmation.');
define('ERR_PASSWORD_TOO_WEAK','An error occured: the password is too weak.'); // See the function secure_password to define a secure password.
define('ERR_LOGIN_NOT_MATCH', 'An error occured: the password does not match the username.'); // Same as ERR_EMAIL_USED
define('ERR_MUST_BE_CONNECTED','An error occured: you have to be connected to access this page.'); // You can give a link to the connection's page.

inscription.php

<?php

session_start();
require_once('fonctions.php');
require_once('constants.php');

if(isset($_POST['confirm']))
{
  $username=htmlspecialchars($_POST['username']);
  $user_email=htmlspecialchars($_POST['mail1']);
  $user_email_confirm=htmlspecialchars($_POST['mail2']);
  $user_password=$_POST['password1'];
  $user_password_confirm=$_POST['password2'];
  $error_message="";

  if(!empty($username) AND !empty($user_email) AND !empty($user_email_confirm) AND !empty($user_password) AND !empty($user_password_confirm))
  {
    if(valid_username($username))
    {
      if(already_used_username($username)==0)
      {
        if($user_email==$user_email_confirm)
        {
          if(valid_email($user_email))
          {
            if(already_used_email($user_email)==0)
            {
              if($user_password==$user_password_confirm)
              {
                if(secure_password($user_password))
                {
                  $error_msg='OK !';
                }
                else
                {
                  $error_msg=ERR_PASSWORD_TOO_WEAK;
                }
              }
              else
              {
                $error_msg=ERR_PASSWORD_NOT_MATCH;
              }
            }
            else
            {
              $error_msg=ERR_EMAIL_USED;
            }
          }
          else
          {
            $error_msg=ERR_EMAIL_WRONG_FORMAT;
          }
        }
        else
        {
          $error_msg=ERR_EMAIL_NOT_MATCH;
        }
      }
      else
      {
        $error_msg=ERR_USERNAME_USED;
      }
    }
    else
    {
      $error_msg=ERR_USERNAME_WRONG_FORMAT;
    }
  }
  else
  {
    $error_msg=ERR_EMPTY_FIELDS;
  }
}

?>

<!DOCTYPE html>
<html>
  <head>
    <meta charset="UTF-8" />
    <title>S'inscrire</title>
  </head>
  <body>
    <div>
      <h2>Inscription</h2>
      <?php if(!empty($error_msg)){echo '<span id="remarque_erreur">'.$error_msg.'</span><br /><br />';} ?>
      <form method="POST" action="">
        <table>
          <tr>
            <td>
              <input type="text" placeholder="Pseudo" name="username" <?php if(!empty($username)){echo 'value="'.$username.'"';} ?> />
            </td>
          </tr>
          <tr>
            <td>
              <input type="email" placeholder="Mail de contact" name="mail1" <?php if(!empty($user_email)){echo 'value="'.$user_email.'"';} ?> />
            </td>
          </tr>
          <tr>
            <td>
              <input type="email" placeholder="Confirmation" name="mail2" <?php if(!empty($user_email_confirm)){echo 'value="'.$user_email_confirm.'"';} ?> />
            </td>
          </tr>
          <tr>
            <td>
              <input type="password" placeholder="Mot de passe" name="password1" />
            </td>
          </tr>
          <tr>
            <td>
              <input type="password" placeholder="Confirmation du mot de passe" name="password2" />
            </td>
          </tr>
        </table>
        <input type="submit" value="Envoyer" name="confirm" />
      </form>
    </div>
  </body>
</html>