This interview was for a GS-1529 (Mathematical Statistician) position at Grade 9, Step 1. I submitted a formatted federal resume on USAJobs.gov in response to a listing, and was contacted by e-mail a few weeks later.
My interview day consisted of three one on one interviews with branch chiefs (managers of approximately 5 to 15 people) among three different divisions of the Bureau, though I later learned that anywhere between three and six interviews is considered normal. Any of your interviewing managers may offer you a position with their branch, but you are most likely to receive an offer from the manager who initiated your interview process (normally the one who first contacts you to setup the interview). All of my interviews were casual, with no questions to evaluate my qualifications and only very friendly questions about my interests and plans. My advice for the interview would be to relax and demonstrate that you are easy to get along and work with.
Regarding the office & culture, my impression is that they parallel closely the interview process. There are a great many people, but the atmosphere is casual (jeans and polos were common at one end of the spectrum, though suit & tie was also a well represented set).
I received an offer from my initiating manager after about two weeks (quite fast for the federal government, really).