See here for more information about registering a domain through WordPress: http://en.support.wordpress.com/domains/.
I don't know about losing traffic, as I believe that your followers are transferred over, so they will still get updates. But views coming from search engines will take a few weeks to start again, as your site needs to be indexed again.
As for links:
New URLs: If you add domain mapping to an existing blog with posts, their URL’s will change. We’ll redirect any visitors looking for the old URL’s over to the new ones, so none of your visitors will get lost out there on the internet, but other services won’t always understand that the old links and the new links point to the “same” place. For example, Tweet counter widgets work based on particular URL’s, so old posts’ counts will be reset to 0. Once you make the change, future posts will not be affected.
The domain upgrade does not change the website in any way, expect for the URL, you are still bound to the same terms of service, and your dashboard and options will all remain the same. Only the URL changes and the .wordpress.com removed.