I used (in 2012) to code with FQL and I was able to make some features such as
FQL query to fetch all data of a facebook page
Actually, FB migrate to graph API.
My question is : Is it possible to retrieve public data of a page (or person) with graph API, even if I'm not a fan of that page (or not a friend )
Yes, everything that you want to do is quite possible with the Graph API. Unless the Page / Group is private, then you will be able to fetch their public data without having to like the page.
https://developers.facebook.com/docs/graph-api
A useful tool that Facebook has provided is the Graph Explorer that allows you to test your queries and see what information will come back: https://developers.facebook.com/tools/explorer
As a specific example that you can fetch without any auth tokens: http://graph.facebook.com/cineplex will return