There are few outside (non-Muslim) sources to corroborate stories of who, and what the first generations of Muslims were. That having been said, Mecca was surrounded by monotheists: Christian Ghassanid Arabs to the north, Ethipia to the southwest. The Jewish Himyarite kingdom on Yemen ended just before the dawn of Islam. In the Hadith we find numerous tribes of Jews in Medina. There are references to Christians throughout the Quran and Hadith, but I've not found anything referring to churches per se. The way the Quran references the Bible definitely implies the Quranic audience would be familiar with the stories in the Bible. Rarely does it repeat the whole narrative, rather it says "Remember this story that illustrates God's mercy? He'll be merciful to you now." "Remember this story that illustrates God's wrath? He'll be wrathful to those who are against him now." So for example:

"Noah cried to Us, and We are the best to hear prayer.

And We delivered him and his people from the Great Calamity,

And made his progeny to endure (on this earth);

And We left (this blessing) for him among generations to come in later times:

"Peace and salutation to Noah among the nations!"" — Qur'an sura 37 (As-Saaffat) ayat 75-79

Either In God's Path by Robert G. Hoyland or Muhammad and the Believers by Fred M. Donner give a good account of the Late Antique religions surrounding the emergence of Islam, although they take them in different ways.

The Qur'an mentions the Gospel. It is called the Injil إنجيل‎ and the fact that it is mentioned in the Qur'an implies that early Muslims did know of its existence and contents. See Qur'an 5.46:

And in their footsteps We sent Jesus the son of Mary, confirming the Law that had come before him: We sent him the Gospel: therein was guidance and light, and confirmation of the Law that had come before him: a guidance and an admonition to those who fear Allah.

The Old Testament is also very similar to the Jewish Torah, which the Qu'ran openly endorses in 5.44:

We did reveal the Torah, wherein is guidance and a light.

There is even a sura (3.3) which appears to advise reading the Torah and the Bible. 'He' refers to Allah in the following passage:

He has sent down upon you, [O Muhammad], the Book in truth, confirming what was before it. And He revealed the Torah and the Gospel.

Did the Prophet read the Bible/Qur'an? The prevailing view, from centuries of Muslim tradition, is that he was illiterate and therefore did not read these texts, much less plagiarise them as has been sometimes suggested. But were the stories in the Bible - especially the Old Testament parts - known to many people through word of mouth? Definitely. The imagery used in the Bible/Torah/Qur'an - shepherds and all - borrows from the real-life experiences of people in the Levant, and though they were written many hundreds of years apart, it makes sense that the same myths and legends would be used as vehicles to explain divine phenomena.