To track people “liking” your page or any other social action you have to add social tracking tags to each and every page and different ones to cover each and every action [Facebook vs Twitter] with the exception of Google+ of course. Hence the lengthy tutorial you linked too.
The alternative is to use a third party social button service that adds tags for you and interfaces with GA in the process.
Once this is done you will see additional social metrics like what you may have now on Google+ actions measuring both the actions and known feedback [remember many social channels are closed vastly limiting what can be read from them].
Nothing to do with GA, but there’s an seo quake toolbar for firefox that tells you a whole pile of things about any site you look at - including number of facebook likes, tweets and plus ones.
No idea how accurate it is, bit early to tell on my site - 6 likes, 4 tweets and 0 +1’s!
Yes, those are just the referred visits from facebook to your site and not likes. If you want to see the likes, you should rather create a page and keep a track of your posts on your page. That would relatively be simple. I’m not sure of any analytic code for likes either.