As to your point 1, I would rather phrase it as a topic of ongoing research. There are some information-based theories that would have something more like entropy being in some sense the underlying law of the universe, and what we currently consider the time-symmetric "base" laws to in fact be the derived laws, in which case in some sense the entropy mystery would disappear. Entropy is a well-observed fact of the universe, and to the extent that our theories fail to explain it very well, that is most likely a problem with the theories, not our observations.