Sassanids are Persians. What would be the difference between Persians and Sassanids? In game Persians reflect pretty well Sassanid Persians with their elephants and elephant bonus.
Where is the difference between Macedonians, Greeks, Minoans? 
Sassanids did not have elephants. 
While Macedonians and Greeks are bit similar, then Minoans are totally different civilization and group. Their society was very different and they were bronze age civilization.
About Sassanid army: Military of the Sasanian Empire - Wikipedia you can read they used elephants.
Yes, although the DE editions go on the other hand, since they are in charge of Forgotten Empires; while Aoe 4 is in charge of Relic…