Note you have "members" and "member" groups. Is this a typo?
It is, a type indeed.
If Sessions and cookies are working the after logging in you should see the logout link.
They work, also the change password fields show correctly.
Make sure that aliases are unique (should pose a problem thought, but it's good to check)
Do I need any aliasses? Friendly aliases? Don't have any turned on.
How does Modx check if a user is logged in? The javascript for the logout link works but for some reason Modx doesn't know that the user is logged in. Can I check the database to see if this is the case? Which tables to look into?