Is it necessary to take both AP Calculus AB/BC and both Physics B/C?

It depends on your major/honours combination.

AP Calculus BC and Physics C are advanced papers that can only be taken by honours students. Theoretically, if you didn't do honours, you can still choose to take the exam, but you have to self-study the content so it isn't really encouraged.

AP Calculus AB and Physics B are regular papers that are practically compulsory unless you have exceptional reasons not to take them. Calculus AB is taken by everyone, because everyone has to take math and learn calculus. Physics B is taken by all physics majors.

In principle all the papers are optional, however, like I have mentioned, in reality, they are as good as compulsory. In any case, most students choose to do all the APs they can because they provide benefits.

First, APs are a standardized exam, so it provides benchmarking for the school diploma. Gets the colleges to realise the rigour of the curriculum: "even someone getting a 3.5/5 CAP still scores 5 (the max score) on an AP". Secondly, most US colleges allow people who score 4 and above on the relevant AP to skip some first-year modules, which is an obvious advantage to the student.

Also, there is financial aid for the APs if your total gross household income or income per dependent is below a certain threshold, so cost isn't too much of a factor.

Dr Hang has said that the school will eventually phase out APs. I think the papers will still be offered but they will truly be optional, not the as-good-as-compulsory policy in place now. This will happen when the rigour of the diploma is fully recognised. However, Dr Hang has only said that it will happen "in a couple of years", so I don't know exactly when.