For your registration with Facebook an email address is necessary. Please retry and give us release for your email address. If you do not have an email address attached to your Facebook profile yet, please add one to your account and try again.
The "stay logged in" button sets a cookie in your browser (for 365 days). This ensures that the website recognizes you the next time you visit it. You can delete the cookie at any time via the settings in your browser. If you share your device with others, you should not activate the "stay logged in" checkbox, as unauthorized users could gain access to your profile and associated data.