It is true that there was no space in the inn, but inn or kataluma in Greek refers to a guest room. So, Jesus would have been born on the lower floor of the house where animals are kept at night. This also explains the presence of a manger.
But, the Bible just mentions that the Magi, came to meet Jesus. They wouldn't have come immediately after Christ's birth, since they found him at home with his mom, not in a manger. And, there's no mention of an exact number; it is assumed that there were three magi, cause of the three gifts.
There are many theories regarding this star. In fact, most point out that it may not have been a star in the first place. It could have been a comet, supernova, or just an arrangement of planets.
The child who finds it on Christmas morning gets an extra present. This is obviously a myth, as it is actually not known in Germany. Moreover, the Germans don't open their gifts on the 25th; they do it on the Christmas Eve.
The myth goes that, the Three Wise Men asked Befana for directions to the birthplace of Christ, but she didn't know. They asked her to join them, but she declined, as she was busy with cleaning. After they went, she changed her mind and decided to look for Jesus. So, she still is looking for him, and gifts kids she meets on the way.
Well, living trees don't combust randomly. The main reasons for fire are defective Christmas lights, candles placed too close, or insufficient watering which makes the tree dry.