I agree Oliver, it does sound very much like a phishing email. Typically these are for banks, but there is also activity for PayPal and eBay itself - haven't had any for years but reported quite a few to that spoof address a few years back.

If you get mail that is unexpected with links that ask you to enter a user name and password, hover over the links first to make sure they take you exactly where you think they should, and not just an address that is close or could be right. It's also very easy to change how a sending email address appears, so check the source to make sure it hasn't been masked to appear genuine.

On the net, I'm afraid it pays to be a little bit paranoid...