I can't understand how the item in that video manages to link to a site outside Ebay - Ebay need to fix this problem fast!
If you ever receive an e-mail asking you to go to either Feepay, or Ebid, or any other site, and 'sign in', first put your mouse pointer over the link and then look at your status bar (at the bottom of the browser window) - this will show you the actual address that the link points to. If it doesn't say
http://www.ebay.co.uk/etc.
or whichever website you're actually supposed to be going to, then it's a scam. It may say "http://www.ebay.co.uk" on the link in the e-mail, but it's easy to make the actual link point to a different website. This is how phishers work a lot of the time.
You should never use a link in an e-mail to log in to a website. Always open a new browser window, and enter the URL you normally enter for the site.
RE the birthdays - where do these occur? It's really bad policy to make it publicly known when anybody's date of birth is, as you say.