I was just checking in webmaster tools and saw that my site now has Sitelinks. Does that mean my site is now an Authority site? Thanks
No. It just means it has sitelinks. That has nothing to do with whether or not the site is an "authority site". It simply means that for certain search terms your site has sufficient backlinks to both the home page and inner pages and a navigation structure that permits Google to offer alternate entries into your site.
You don't. Google may have a definition for it but they're not saying, beyond a patent application from a few years back.
That's good, but it doesn't mean you're an authority site at all. They're two completely different things, but, congrats!
the strange part is that when i search for my domain google i do not see the sitelinks but i see it in webmaster tools. Maybe after the next serp updates?
try logging out if logged in. use the keyword list google gives you to look for your site... I believe the display is when a keyword search is done, if I am not mistaken.