If the police ask you questions, tell him you will not answer any questions without your lawyer present and that he should either arrest you or let you go.
You are required to carry the registration on the bike at all times. I would just pull the information out and show him. It is not the law that is confusing, it is the police not knowing what the law actually is that causes the problem.
You may pass on the right, ride in the bike lane etc.
I usually just stay in the lane and move with traffic. I usually do this because it pisses off bike riders when we are tailgating them (I don't blame them) and I have seen too many dooring accidents. Several years ago a bike rider was doored and pushed under a city bus.....you don't want that to be you.