Is $0^{\sharp}$ the minimal assumption to prove consistency of light\heave class dichotomy theory?

Two questions to be raised about the theory presented in posting about the class theory with light\heavy class dichotomy. There the question was answered to the positive, i.e. the theory is consistent relative some large cardinal hypothesis, that of the existence of $ 0^{\sharp}$ . The two questions are:

  1. Is existence of $ 0^{\sharp}$ the minimal large cardinal hypothesis under which this theory is provably consistent?

  2. Which kind of Ontology bears the existence of large cardinals in that theory, is it light sets, or heavy sets or proper classes?