1. No there isn't
2. The game starts in 272 BC. When Alexander the Great died in 323 BC he already had conquered Persia, so this faction does not exist in the form you seek. The Arche Seleukeia, who is one of Alexanders Successor-States, covers a great part of the former persian empire.
3. The Koinon Hellenon. I'm not sure, if the Makedonians and Epeirotes also can field Spartiatai Hoplitai after having conquered Sparta and installed a type IV governement.