Was Heraclius a Melkite, and what is Melkitism, when did it begin and when did it end, and is it different from Catholicism?

We do not have anything definitive regarding this. We advise the questioner to occupy themselves with what is important to them and their nation, which is learning the texts of the two revelations (Quran and Sunnah (definition)). Ignorance of these matters does no harm, and knowledge of them brings no benefit. As for the Melkites, they were a party to the imperial state's doctrine. Emperor Heraclius attempted to unite the clashing doctrines of the state. There is a difference in belief between the Melkites and the Catholics.