Item #1: Now I may be revealing my own ignorance here but, I never knew what the significance of the twelve days of Christmas was, I mean besides a fairly annoying Christmas carol. It is the time between Christmas the the celebration of the Epiphany....
According to Wikipedia, The term epiphany means "something that is shown" or "made known" or even "revealed." In Western churches, it remembers the coming of the wise men bringing gifts to visit the Christ child, who by so doing "reveal" Jesus to the world as Lord and King.
It is celebrated on Jan6, twelve days after the observed day of Christ's birth.
Item #2: The Immaculate Conception was not the conception of Christ by the Virgin Mary as many believe. Nor is it, as Pittsburgh Steeler fans would argue, the play, guided by divine intervention, in which Franco Harris scooped up a defelected pass by Terry Bradshaw and ran for a touchdown to beat the Raiders. That was the immaculate RE-ception. It describes the birth of Mary, who supposedly lived her life without sin, as she was chosen by God to be the mother of Christ on Earth.
Item #3: The Yule log is a Norse, pagan ritual through which sacrifices were made to the god of fertility over twelve days. The log was decorated and was supposed to burn in the fireplace for all twelve days or it would displease the god.