A real "Stay signed in": keep the connection

Instead of trusting the php session, it uses a cookie. The php session
sooner or later is distroyed if not used. It depends upon the server
settings. Using a cookie ensures that one really stays signed in.

Dev notes: I wanted to avoid merge conflicts, stay with the main
developper standards and keep the "index.php" in one file. That's why
the code may not be that nice. My own dev level my also explain.