What language did the eastern empire use?

Greek

In 395 AD when the Roman Empire split into western and eastern (Byzantine), Latin continued to be used as the official language but in time it was replaced by Greek as that language was already widely spoken among the Eastern Mediterranean nations as the main trade language.

monarchy doesn’t have to have the hereditary element. there have been elective monarchies in the past where you choose your king-for-life and when he dies elect someone else for the job.

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