Your "you can't even give us an exact date for St Cyril's birth" is simply you being ignorant. Putting a question mark after someone's birth or death date simply says that the date is unknown. It should not surprise anyone that birth records from 4th century Egypt don't exist.

Cyril's life and character are both well known. As a young man, he participated in the railroading of John Chyrsostom, to distract people from charges of fiscal mismanagement by his uncle Theophilus. He deliberately misstated the views of Nestorius, and did not give Nestorius a proper chance to defend himself at Ephesus (and excluded John of Antioch for coming a day late to the council). He expelled the Jews from Alexandria. He incited the mob who lynched Hypatia, the head of the Neo-Platonist school.

All of these are well known to anyone who has studied Church history.