This is depends on our use, people what they need they will search for that. I don't know exactly most searches on FB, I am also waiting for the answers form DP.
You can't predict what people are going to search on Facebook. This usually depends on the mood of person using Facebook but if you still want my view than for now i would search for SEO tips and tricks ....
nobody knows..it depends upon user what they want.. Different people search different things on facebook..
Good suggestion to go with SEO tips, because it is hard to tell what people are searching on any given day. Facebook Insights gives you a good idea about what is happening with your pages. Great analytic tool. I've also been using Hootsuite to optimize my social networking efforts in which I may monitor when keywords I enter are being mentioned and to find top influencers who can help to amplify my message. They also have some analytics that are dynamite at giving indications of where people are and what they are looking for.