The idea is to allow new users to signup without sending a confirmation e-mail.

So, in the "config_inc.php" file I've put the following line

$g_send_reset_password = OFF

When an user Signup for a new account, should type an Username (the Email is not required anymore)

Results:

1) The following message shown in the form shouldn't appear [BUG]

On completion of this form and verification of your answers, you will be sent a confirmation email to the email address you specified.
Using the confirmation email, you will be able to activate your account. If you fail to activate your account within seven days, it will be purged.
You must specify a valid email address in order to receive the account confirmation email.

2) The e-mail is not sent [OK]

3) The user can't login [BUG]

Your account may be disabled or blocked or the username/password you entered is incorrect

I've looked in the data base (MySQL) and a password has been inserted but it's not "blank"

Thanks