B Is it possible that god does not play dice with the universe, as einstein said?

Sure, there could be information and relationships which are not known to us. They must include non-local components if causality is to be retained (per Bell's Theorem).

 

Some interpretations of quantum mechanics do not have randomness. If you look at the table in https://en.wikipedia.org/wiki/Interpretations_of_quantum_mechanics
the first column is deterministic.

For the most part, if a collapse of the wavefunction occurs, then it is a random process. But if there is no true collapse of the wavefunction, only an apparent one, then it is deterministic.

It's not easy to test these interpretations, which is why they are called interpretations and not theories, but people do sometimes claim to test decoherence, which seems to be the popular belief these days.