Yup. Flickr can get the job done.

Try using different browser

Use it only for finding peoples info purposes. It work most of the time easily.

Is it permanent feature? So it will block you from requesting other people if you don't provide enough to prevent spamming

I think if you login your Facebook account on other computer at same time, one of the account will auto log off.

You can get this feature in Facebook Friends Checker for a Chrome extension

Facebook has a new registration tool to make it easier for users to sign into other sites. With the new registration tool, users can sign-in to an outside website using your Facebook account.

The new registration tool works like an auto-fill tool automatically fills the registration form with user's Facebook information, like name, email address and location.