The warning at the top of that login / registration screenshot says that the email address is already registered. This means you already have a Joomla account with that email address. You can try setting the JFBConnect backend > Configuration > General > "Automatically Link Users by Email" to Yes. Then when you click Login with FB button, the account will automatically be linked to the existing account. You will not proceed to the login/register view. Since it's at No now, you're brought to the Login / Register page and have to enter the existing username and password into the form, as shown in one of your screenshots, to map the social account to the existing account.
-Melissa