1 Who was the first person to be told the news about the coming of the child Jesus? And where were they?
Was it Joseph? Or Mary? And were they in Nazareth? Or in Bethlehem?
According to Luke, it was in Nazareth, in the northern region of Galilee, that an angel named Gabriel appeared to Mary, to inform her that she would bear a child (Luke 1:26). That is different from the story told in Matthew’s Gospel, where an unnamed angel delivers the same message, not to Mary, but to Joseph, to whom she was engaged (Matt 1:18).
The location of the announcement in Matthew’s account is not specified, but it is reasonable to assume from the flow of the narrative that this took place in the southern region of Judah, in Bethlehem (Matt 2:1, 6). Matthew, having located the family initially in the southern city from the beginning, has no need of the story of a census and a forced trip from Nazareth to Galilee (Luke 2:1-4). The family is already in Bethlehem, another small village, but in the south, in Judea.
So we have two versions, with significant differences.
2 Were Joseph and Mary travelling while she was heavily pregnant?
The story told by Luke reports a widespread movement of the population that meant a pregnant Mary from Nazareth, accompanied by Joseph, had to travel afar and find lodging in the crowded town of Bethlehem just at the most inconvenient time—because “a decree went out from Emperor Augustus that all the world should be registered” (Luke 2:1).
There are historical problems with this story. Identifying the census as an actual historical event, and locating it accurately in time, both present challenges. There is no other record of such a Roman census at that time. King Herod, noted as ruling at Luke 1:5, and also at Matt 2:1, died in 4BCE, but Quirinius, who ordered the census noted in Luke’s account, began as Governor in 6 CE.
Even though the combined story has entered the popular mindset as a real event and provides a clear and compelling picture of the holy family as travelling far when Mary was at term, because of decisions made by political authorities, whether Herod or Quirinius, we can’t say that it actually took place. So the answer is, a very hesitant, maybe.
3 Was it actually a “silent night”?
No: it is not the case that “all was calm, all was bright”, that it was a “silent night”, that the cattle were gently lowing and “the little Lord Jesus … no crying did make”. Lots of travellers and inns that were full would surely mean the town was abuzz? This was no irenic scene, such as we see on Christmas cards and sing of in Christmas carols.
Mary giving birth would surely have meant that it was not, in fact, a silent night. Labour without any modern medication would have been primal and harsh. The arrival of the child was surely signalled by that first hearty cry of a newborn, piercing the other sounds of the noisy night.
Although the Bible is silent on the matter, the Quran reports of Maryam (Mary), “The labor-pains came upon her, by the trunk of a palm-tree. She said, ‘I wish I had died before this, and been completely forgotten’” (19:23). The Bible does not mention any labour pains or any physical pain in the birth narratives. But let us not think that it was a silent night—in all probability, it was very noisy!
See https://johntsquires.com/2019/12/18/no-crying-he-makes-get-real-puhhh-leeeease/
4 Was Jesus born in Bethlehem?
Matthew and Luke claim that Jesus was born in Bethlehem, in Judaea. No other biblical reference agrees with this, however. In fact, in his adult life, Jesus was known as “Jesus of Nazareth”, a town in Galilee (Matt 21:11; Mark 14:67; Luke 24:19; John 1:46; Acts 2:22). He is identified as a Galilean (Matt 26:69; Luke 23:5–7). There is no mention of his birth in Bethlehem outside the accounts of Matthew and Luke. His home is in Nazareth, and he spends almost all of his life in Galilee. The answer to this question is No.
So why do two writers claim that he is a Judean? One clue can be found in John 7:40–43, which indicates that Jewish people expected the Messiah to be born in Bethlehem, of the line of David. This view is based on the prophetic word of Micah 5:2, “from you, O Bethlehem Ephrathah, shall come forth one who is to be ruler in Israel”. This is precisely the way Matthew and Luke tell it. Jesus is born in Bethlehem. However, no other biblical writers know anything of this story.
It appears that Matthew and Luke have shaped their versions of Jesus’ birth so that it accords with traditional Jewish expectations. They do not recount precise historical information. Rather, they tell a story in such a way that it implicitly meets expectations about Jesus. And so, because he allegedly comes from Bethlehem in Judea, they can claim that he is the Messiah.
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See also https://johntsquires.com/2021/12/20/questions-about-christmas-interrogating-the-biblical-story-2/
https://johntsquires.com/2021/12/21/questions-about-christmas-interrogating-the-biblical-story-3/
https://johntsquires.com/2021/12/22/questions-about-christmas-interrogating-the-biblical-story-4/
An Informed Faith 
Concerning the census of Quirinius, I take into account Luke’s intent to address his Jewish readers in an article you may find of interest. The journey to Bethlehem in Luke’s story of the first Christmas is motivated by the Roman census. Jewish readers of Luke in the first century would remember the census as connected to the Jewish Revolt of the year 66. How would they have reacted to Luke’s use of this event? See my article “The Christmas Journey and the Jewish Revolt”, at http://josephusblog.org/the-christmas-journey-and-the-jewish-revolt/.