Using PHP 5.5's password_hash and password_verify function

Ignoring the issues with your database statements for now, I'll answer the question regarding password_hash.

In short, no, that is not how you do it. You do not want to store the salt alone, you should be storing both the hash and salt, and then using both to verify the password. password_hash returns a string containing both.

The password_hash function returns a string that contains both the hash and the salt. So:

$hashAndSalt = password_hash($password, PASSWORD_BCRYPT);
// Insert $hashAndSalt into database against user

Then to verify:

// Fetch hash+salt from database, place in $hashAndSalt variable
// and then to verify $password:
if (password_verify($password, $hashAndSalt)) {
   // Verified
}

Additionally, as the comments suggest, if you're interested in security you may want to look at mysqli (ext/mysql is deprecated in PHP5.5), and also this article on SQL injection: http://php.net/manual/en/security.database.sql-injection.php

Using your own salt is not recommended and, as of PHP 7, its use is deprecated. To understand why, the author of password_hash shared these thoughts (link defunct)

One thing has become abundantly clear to me: the salt option is dangerous. I've yet to see a single usage of the salt option that has been even decent. Every usage ranges from bad (passing mt_rand() output) to dangerous (static strings) to insane (passing the password as its own salt).

I've come to the conclusion that I don't think we should allow users to specify the salt.

He even made this comment in SO chat noting how bad passing your own salt can be

Note this from php.net

Warning

The salt option has been deprecated as of PHP 7.0.0. It is now preferred to simply use the salt that is generated by default.

Conclusion? Forget about salt option.

This would be quite enough password_hash('password', PASSWORD_DEFAULT) *(or _BCRYPT)