I found the source of the problem #2. It is the use of *session_register(foo)*.
I put the following to my *handle_registration.php*.
session_register("foo");
session_register("foo2");
$foo2 = $_POST['email'];
$foo['email'] = $_POST['email']
The problem still persists, since no variables are stored to my session cookie.
This is the logic of my login script.
- Solved by Pascal Martin and The Disintegrator: Which is the right place to put the function 
session_write_closein generating sessions for login? - How can you get a permanent session for user "session" such that a new session is not started each time index.php is loaded?
 
I have the session_start() at the beginning of my index.php. 
The very Beginning of my index.php
 session_start();       
 if($_SESSION['logged_in'] == false) {
     $random_number = rand(1,100000);                                                       
     session_id($random_number);
     session_id['email'] = '';
 }
while the very end of my index.php
<?php
session_write_close();        // Session code ends here!
?>
I have right after the very beginning of the session code the validation process of user's password by
 $dbconn = pg_connect("host=localhost port=5432 dbname=masi user=masi password=123");
 $result = pg_prepare($dbconn, "query22", "SELECT passhash_md5 FROM users
         WHERE email=$1;");
 $passhash_md5 = pg_execute($dbconn, "query22", array($_REQUEST['email']));     
 // users from registration/login form
 if ($passhash_md5 == md5($_REQUEST['password'])) {
     $_SESSION['logged_in'] = true;
     $_SESSION['email'] = $_REQUEST['email'];
     $_SESSION['passhash_md5'] = md5($_REQUEST['password']);
 }
 // this may be unnecessary if the passhash_md5 cannot be changed by the user 
 $passhash_md5_2 = pg_execute($dbconn, "query22", array($_SESSION['email']));  
 // users staying in the site
 if ($passhash_md5_2 == $_SESSION['passhash_md5'])) {
     $_SESSION['logged_in'] = true;
 }
The code generates me continuously random sessions such that no user's data is being saved for the user. 
I replaced each $_REQUEST after the login/registration handlers by $_SESSION in my code, since $_REQUEST does not include $_SESSION - still the same problem and I cannot see the username in the homepage after registration/login.