I have people who "like" my posts (friends of fans), but never become fans of my actual page. Is there a way to invite those people to become fans of the page?
There's no way for you to directly contact someone on FB who liked any of your posts, and if there was, it probably would be considered spam - you could try running a paid ad to "friends of fans" inviting people to like your page though!
I also put a link when I update my tracking numbers to customer's saying something along the lines of, "Thank you for the order. Hope you come back again. If you like us, like our fb page." than i link it.