Occams razor btw is a direct consequence of bayesian statistics. In that method of forming theories to explain observations nothing can even be ruled out or proven. If you believe that the earth is flat, then for you the earth is flat. But it may require some extremely fine tuned math to make all observations consistent with that theory. But if you start with the idea that the earth may 50% be flat and 50% round, then the simplicity of the sphere assumption will tell you to use that model.

On quantum mechanics particle vs wave in my opinion the problem is the limited human mind. In everyday life we know only particles and waves. Now we make experiments and find something entirely new. But in some special cases it may behave as a particle or a wave. It does not mean it is either, in fact it is neither, it is just a quantum object that has no working classical analogy.