All perfect praise be to Allah, The Lord of the Worlds. I testify that there is none worthy of worship except Allah, and that Muhammad, sallallaahu 'alayhi wa sallam, is His slave and Messenger.
What we have found in the biography of Bilaal is that his mother was Abyssinian. She was a freed slave woman, previously owned by the Banu Jumah clan, and her name was Hamaamah. As for the color of his eyes, no mention was made of it in the books we have consulted. It is known, however, that he had dark skin, and he will be ahead of all the dark-skinned people in entering Paradise, as narrated in a Marfoo’ narration (a Prophetic narration). His merits and virtues, may Allah be pleased with him, are well-known. It is enough as merit that the Messenger of Allah gave him glad tidings of entering Paradise, and asked him about the act that he performed for which he was most hopeful of being granted such a great reward, so he told the Prophet that whenever he performed ablution he would perform such a number of prayers as was written for him to perform. [Al-Bukahri and Muslim]
As for the reason he was chosen to be a Mu’aththin (the person making the call to prayer) it is because he had a more beautiful or louder voice than the Companion who saw a vision about the Athaan (the call to prayer), namely, ‘Abdullaah ibn Zayd . Abu Daawood narrated that the Prophet said to ‘Abdullaah ibn Zayd, when he saw a vision about the manner of performing the Athaan: “Go to Bilaal and teach it to him, for he has a better voice than you.” As for the claim that Bilaal, may Allaah be pleased with him, was the only one who was granted permission to stay with the Prophet during his time of retreat, it is not true.
There is no doubt that Bilaal was tortured for the sake of Allah, The Exalted, and this was one of his greatest merits and virtues.
For more benefit on a short biography on Bilaal please refer to Fataawa 387274 and 45237.
Allah knows best.