Were the Persian empire's people assimilated into a homogeneous group?

No, they were very diverse. The Empire stretched from today's Libya in the west to Pakistan in the east. They represented a wide variety of ethniciities, languages and cultures, different from those of today, but just as diverse. And thwhile the Persians tried to encourage civilising influences, they left local people to their own leadership style and culture, under Persian provincial control. They did introduce Aramaic as a lingua franca to facilitate communication, but the bulk of the peoples retained their own politics, organisation and customs and language.