Ajax User login failing with "Username field is required", "Password field is required"
It looks like user_login_submit doesn't work well when called as an AJAX callback. The error you receive is because Drupal tries to create a session for the user that should be logged in, but no values for uid is present, which is required.

I believe that Drupal will call the form submit hooks when the form is submitted by ajax, so you might be able to simply add an empty callback function.

Alternatively you will need to call the form submit functions yourself, which should fix the problem.