Can the user change the session content? (for example, if user is logged in and $_SESSION["username"] is "example.com", can the user change the session $_SESSION["username"] to "example.org" to ruin another website?
No. Sessions are stored on your server thus it would be impossible to directly change the session. On the other side, it all depends on the developer and how the interprets the client requests. For example, making
$_SESSION['last_website'] = isset($_SERVER['HTTP_REFERER'])
? $_SERVER['HTTP_REFERER']
: $_SERVER['REQUEST_URI'];
would eventually override the $_SESSION['last_website']
.