First of all, Merry Christmas one and all, whether Christian or not. This is a time of year to celebrate family, generosity, peace, and love.
Now to the mysteries:
The Star of Bethlehem and the 3 Magi. This mystery comprises the fact that very sophisticated cultures existed in the East, whose knowledge of astronomy was far advanced. There are many theories as to what this mystery is about - the meaning of the gifts etc. Personally I am inclined to think that Johannes Kepler- the astronomer who discovered elliptical orbits hundreds of years ago - was on the right track with the notion that the Star was a “stellium” or conjunction of planets.
King Herod and the Massacre of the Innocents. There is no outside source to corroborate this story, and so it is sometimes regarded as allegorical and not historical. However, Herod is known to have killed family members, and the Old Testament is full of massacres, so my sense would be that it likely does refer to a historical event.
“Jesus died for your sins.” This is an Easter mystery, but if one considers the Hindu concept of karma, and whether it is possible for another being to “take on” the karma of a group, then Jesus’ sacrifice can be seen in this light. A Hindu perspective on the matter is at https://www.speakingtree.in/allslides/jesus-christ-revealed-from-the-hindu-vedas/49602.
Tying item 1 and item 3, while the Bible makes no mention of India, there are accounts asserting that one Magus was from India. St. Thomas is reputed to have travelled to India and died there. It is quite likely that there was both commerce and exchange of ideas between Israel and India during the era of Jesus. The art of astronomy/astrology in Hinduism, jyotish, is incredibly rich in history. It is not inconceivable that a Magus with knowledge of jyotish could have been among the 3 Magi.
Typing on smartphone and unable to edit - it’s Johannes Kepler
I recall Roy Amore of U of Windsor making a case back in the 70s of not only the possibility of Buddhist sayings being incorporated in the gospels due to a caravan route between what is now the Middle East and India but also the probability. Similar to how the writers of Mathew and Luke had Q before them, the Buddha too, relied on Q. Q meaning Quelle which in biblical studies is regarded as a common source for the synoptic gospels.