What are these?
Hanukkah is a little different. Did God ordain it?
No, Chanukah is not biblical in origin.
This was a main point of my questions. are Hanukkah and Dec 25th related?
Well, it is possible that the 25th of Kislev did occur on what was to be Dec. 25, but that calendar wasn't in effect at the time.
The Feast of Christ's Birth was celebrated on Jan 6 because a Roman feast occurred at the same time. The Romans weren't happy about "other" feasts occurring at other times so the Christians held their feasts at the same time as the Romans so as not to arouse suspicion.