1. I didn't know the existence of "BP" until just a few minutes ago, but I just looked it up and it stands for "Before the Present" -- so it's a synonym of BC. This is done because "BC" refers to Christ and the Christian religion, and for the sake of political correctness many people want to avoid such references. The more common alternative, though, is "BCE", which stands for "Before the Common Era".
2. You can say, for example, "If you will sit down for a moment", which means something like, "If you would be so kind as to sit down", except it's a little more forceful. Another possibility: "If you will smoke", which means: "If you insist on smoking". Notice that in this construction, we often stress "will"; it implies that the person being addressed only has him or herself to blame: "If you will smoke, you shouldn't be surprised when you get lung cancer." Very often, as in this case, "will" is connected with the idea of a conscious decision: smoking is your own deliberate choice.