They were popular rulers because they both did something important. Constantine made Christianity legal, and Justinian made a code of laws and built the Hagia Sophia. People respected them for that.
Theodora was important to Justinian's rule because during the Nike riot, she told Justinian to send troops to kill rioters in the Hippodrome.
Hi, im Theodora, before I married Justinian, I was an Actress, or at the time, a prostitute.
Justinian's code was a list of laws that made rules governing assault and battery and marriage. Many countries made their law the basis of Justinian's code because the laws were very good at making peace and stability.
Icons are religious images like Jesus and the cross, like in Christianity.
The Byzantine Empire preserved Greek and Roman ideas because they spoke Greek and they built building based on Roman Empire.
The real problem that affected the Byzantine Empire was pressure from the Ottoman Turks. It was a problem because they were weak from their fight with the Seljuk Turks. The Seljuk Turks also helped to bring the fall the Byzantine Empire.