Parents/siblings - Moriarty had his parents and two older brothers killed because with them in the way, he would never be “head honcho” in the Moriarty family. His father was at the top and also his mother by marriage, then came his oldest brother and second oldest brother, both of their names are unknown due to their parents keeping them entirely out of the system. Because of this, he got rid of his brothers, doing it so well not even his parents suspected him. He soon realised that his parents weren’t going to back down from their position for another good few years, since they were young parents. So he got rid of them. The lower-ranks realised it was Moriarty but did nothing to remove him of his position. By the age of only 12, Moriarty was the head of the biggest and most wanted crime family in the world.
The year and a half long absence - Moriarty left of his own accord because of the duties of being at the top was too much. He left to hire someone that he could trust - to the extent that Moriarty trusts - to be second in command and help until he left Hogwarts. The second in command, Sebastian Moran, does not know that Moriarty will have him killed the day he graduates.