Regarding the Trinity and the Quran.
Here's an interesting article:
TRINITY IN THE QUR'AN: A HISTORICAL ACCOUNT by Media Zainul Bahri
The following two paragraphs are a shortened version of the abstract (1) and the conclusion (2):
1.1 ... Theologically, what is meant by the Trinity in the Qur'an is a belief in three Gods: God (Allah), Jesus (Isa), and Mary, as the three independent Gods, while the (orthodox) Christian belief confirms that God, Jesus and the Holy Spirit (not Mary) are one God, not three independent gods.
1.2 ... Historically, the explanations of Olaf Schumann, Parrinder, Kurt Aland, Anton Wessels, and Fazlur Rahman, indicate two important things. First, the Christians in Arabia and whom Muhammad met in Mecca and Medina were dominated by the Nestorians who emphasized the humanity of Jesus and the One Almighty God. That is why the Qur'an sharply criticizes the system of the Trinity and the divinity of Jesus and Mary. However, both Schumann and Parrinder believe the Qur'an's criticisms of Christianity are misdirected, in a sense not to the official Christian Trinity doctrine.
1.3 ... Second, since Mecca is a very international, there are probably many Christian people or communities with different streams. But, as Schumann stated, they were merchants, not theologians. Schumann, Parrinder and many Christian and Jewish scholars agreed that the Christian and Jewish communities in the time of the prophet subjected to criticism of the Qur'an are sects deviating from the legitimate doctrine.
1.4 ... Moreover, when the prophet lived, there had been no acceptable philosophical explanations of the great thinkers concerning the doctrine of both Jewish and Christian monotheism to those who were thoughtful. In other words, the prophet only heard and received any information about the theology of both Christian and Jewish from ordinary people or priests who were not master at esoteric knowledge.
2.1 ... This means Muhammad came to Jewish and Christian people who are deviated from the official doctrine as formulated in the Council of Nicea in 325 AD.
2.2 ... Accordingly for Schumann, the Qur’an accounts of Jesus or Mary do not correspond to the Old or New Testament which may not have been translated into Arabic, either in part or in whole. Furthermore, the details of the Qur’an versions are similar to those commonly found in Christian or Jewish apocrypha, i.e. uncanonized books and those from ordinary Christians. In other words, there were already popular theology books or at least a popular understanding of Christianity, which are not the work of Christian theologians due to many innaccuracies teachings. In fact, the books often contain unfinished theological problems, and emphasise more on exciting and magical things to hear than the true theological meanings.
A comment on this last: It is evident that the islamic commentaries on the crucifixion that they are informed by Gnostic and apocryphal texts which focussed more on the 'magical' and 'esoteric' than the orthodox belief ... that Jesus was not crucified, that an angel took his place, or another, who was magically made to look like him ...
Similarly, the childhood stories of Jesus are drawn from a number of apocryphal texts in which the boy Jesus performs miracles and murders in equal measure ... the murderous elements were left out ...