by providing useful and attractive info yo may get more visitors and increase friend request since u have chance to get more likes for your page and also create a separate blog with valuable info and embed the link of fb over there........
You can take paid services to increase your fan page likes else you can make you fan page attractive which is like by people and share some interesting stuff on your page and be active while interacting people by replying and comment etc. Post some contest on your fan page for fans weekly or monthly.
i also want to get natural real likes that they acutally also comment and chat on our page, they seem not in the mood of talking, try to sign up for groups, and find other relative groups to join, but also the system do not allow us to send messages to those group admin.
You can increase your facebook likes by first circulating the links in your friend circle and then by circulating to more and more people you know . Also you can share it on forums of respective fields.