I want to know about the religion followed by these kings (& others if there were any) who sent/gave gifts to our Prophet, sallallaahu 'alayhi wa sallam: Were they Jews, Christians, idolators or did they follow another religion? Also, what was the religion of Ayyaad ibn Himar when he gave a gift to our Prophet, sallallaahu 'alayhi wa sallam, and he said to him, "I have been forbidden to accept the gifts of the mushrikeen (polytheists)." [Abu Dawood & al- Tirmidhi) What does the word 'mushrikeen' mean in this hadith? (Does it mean Jew, Christian, idolator or what?) Why did the Prophet, sallallaahu 'alayhi wa sallam, not accept his gift? I do not know whether I may have repeated the same hadith, and please note that I shortened some (or all) of these hadiths. Al-Bukhaari and Muslim narrated that Ukaydir Doomah offered a gift to the Prophet, sallallaahu 'alayhi wa sallam, and that he accepted it. He also accepted the gift given to him by Muqawqis, who was the king of Egypt. [Ibn Khuzaymah and others] The ruler of Persia sent a gift to the Allaah’s Messenger, sallallaahu 'alayhi wa sallam, and he accepted it. The ruler of Rome sent him a gift and he accepted it. The kings sent gifts to him and he accepted them all. [Musnad Ahmad (1/96). See also Sunan al-Tirmidhî (1576)] The ruler of Doma (in Syria) gave a gift to the Prophet, sallallaahu 'alayhi wa sallam. [Sahîh al-Bukhârî (2616) and Sahîh Muslim (2469)] The king of Aelia gave the Prophet, sallallaahu 'alayhi wa sallam, a white mule and a cloak, and he (the Prophet) approved of him as the ruler of his land. Narrated by al-Bukhaari (2990) The Messenger of Allaah, sallallaahu 'alayhi wa sallam, was riding a white mule of his, that had been given to him by Farwah ibn Nufaathah Al-Judhaami. [Narrated by Muslim (1775)] I need to know about the religion followed by all of these kings (and others), seperately and completely. I need this information for some important purpose. Please note that I concern myself with authentic hadiths only, and if any hadith (mentioned above) is not authentic, then please do point out to that. May Allaah reward you.

All perfect praise be to Allaah, The Lord of the Worlds. I testify that there is none worthy of worship except Allaah and that Muhammad is His slave and Messenger.

Mentioning the details of the religion of these kings and others is not the nature of the fataawa at Islamweb, but you can find such details in books of biographies, history and interpretations of ahaadeeth. Nonetheless, we will mention the religion of those whom you mentioned in the question in brief.

As for Ukaydir Domah, who was the King of Domah, then Ibn Hajar said in al-Fath, “Domah is a country between Hijaaz and the Levant, and it is Domat Al-Jandal, a town near Tabook; it has palm trees and plantations, and a fort, at ten marhalahs (one marhalah equals 8 farsakh, each farsakh equals 3 miles) from Madeenah and at eight marhalahs from Damascus. Ukaydir was its king, whose name is Ukaydir ibn Abdul Malik ibn Abd Al-Jinn ibn A'baa' ibn Al-Haarith ibn Mu'aawiyah; he is traced back to Kindah, and he was a Christian.” 

The Muqawqis, the King of the Copts, was a Christian.

Kisra, the king of the Persians, was a Maji.

The Emperor Heraclius was a Christian.

The king of Aylah was a Christian.

Farwah ibn Nufaathah was a king of part of the Levant in the pre-Islamic era of ignorance; he was a Christian, then he became a Muslim.

As regards 'Iyaadh ibn Himaar, he was a pagan, and he was an old friend of the Prophet then he became a Muslim.

As for why the Prophet did not accept his gift at the beginning, then Al-Khattaabi said in Ma’aalim as-Sunan:

“There are two reasons for him refusing his gifts: one reason is to make him angry by refusing his gift and that this would be an admonition for him; this would lead him to embrace Islam. The second reason is that the gift affects the heart, and the hadeeth reads, 'Exchange gifts, you would love each other.' But it is not permissible for him that his heart would be softened towards a polytheist, so he refused the gift in order to eradicate the reason of being sympathetic towards him. It has been proven that the Prophet accepted the gift of An-Najaashi (Negus), and there is no difference of opinion about this, as he said, 'I was forbidden from taking gifts from the polytheists,' as An-Najaashi was a man from the People of the Book, and he was not a polytheist. It is known that we are permitted to eat the food of the People of the Book and marry their women and that this is contrary to the ruling on the (food and women of the) polytheists.”  

It is clear that the word mushrik (polytheist) in the hadeeth of Iyaadh was interpreted by Al-Khattaabi to refer to the polytheists other than the People of the Book, but there is a difference of opinion on the issue. Ibn Hajar held the view that, “The opinion of those who interpreted refusing the gift to apply to the idolaters only apart from the People of the Book is invalid.” 

Allaah knows best.