Available data about 'likers' as a page on Facebook
Want to wish you good luck. Some time ago faced with the same problem, but didn't find any satisfying solution. 
First of all, there is no way to get list of users, who "liked" a particular page. Even, if you are an administrator of this page (I was). One only can get list of last 3 or 5 hundred users. 

Friendships data for most of the users is also inaccessible. Looks like gender is the only thing from your list, that you can get. 

Data about pages, that exact user "likes", should be available (as it's written in docs), but in reality, through API you can collect something only for friends and FoF. Even though this data is available through web interface. So the only way is to try dirty trick with parsing and scraping (but remember, that I didn't advise it ;) ).