I would agree with Cecilia_Writer and even go a step further. If you want to use FB for business purposes, an author page is essential. I don't know the details, but I do know there are FB regs that frown on commercial activity from a personal profile.
Giveaways are never a bad idea, but they can draw people who are only interested in the giveaway, as opposed to people who might actually be interested in your writing. The best long-term way to draw real fans is content. Find things to post that your type of reader might find interesting. If all you ever post is ads for your books, you won't attract that much attention. (I've heard ratios like 7 to 3 or 9 to 1, non-commercial to commercial content.)
I post about my books when something is happening, like a new release or a great bargain. Otherwise, I post other content related to my genre when I can find it, items that express my sense of humor or philosophy when I can't.