While Facebook insights provide demographic details and interactions on the fan pages but are still limited as compared to Google Analytics. Yes, you can set up Google Analytics for your facebook fan page and get all the details that a analytics account provides you.
Here is how you need to do it:
1) Setup Google Analytics account. If you already have one, create a new website profile. You can name it facebook.com or facebook.com/your_page_name. You will finally get your tracking code which looks like this UA-3123123-2
2) Create your custom img tag for each of your pages you like to track. EG: contact form, services, products etc. You can use our tool to create the Google Analytics link generator for Facebook pages.
3) Add the entire custom image html tag from step 2 to the bottom of each Facebook fan page that you need to track.
That is all you need to do! Google Analytics is not real-time, so you will need to give it some time…approximately a day.