How to use Facebook API to send invitations to friends to ask for a specific fanpage like.
And the other question.
How then show a list of users who have sent an invitation with an indication of how many people liked the profile. In this way, users will take a ranking of who sent the most invitations
You may use the Notification API, with a message and the link to page. Or, using the Feed dialog by posting on wall to each of the app user. (I prefer the first one)
The invitations will be sent to all the friends I guess. If not, then you have to keep the record of the invitations sent, manually.