I think the tradition of gift-giving on Christmas originated before the time of Nicholas.
The Magi (Wise Men or Kings) brought the Christ Child gifts of gold, frankincense and myhrr (sp?). That began the tradition that Nicholas popularized. Incidentally, we don't know if there were really THREE Wise Men. There could have been more or less.
It's just that the Gospel tells of three gifts so the tradtion of THREE Magi developed. Also, the Magi arrived some time after Jesus was born. It took quite a while for them to follow that star. Matthew's gospel indicates that Mary and Joseph were not living in a stable when the kings arrived, but had settled into a "house".
No, Jesus was never a formal rabbi. He was a teacher, but doesn't "rabbi" mean "teacher" in Hebrew?
"Long live God!" (GODSPELL)