Dear rabbi. I have been studying the noahide laws since a couple years ago and tried to keep these holy mitzvot as good as possible. This year there arose a question since my child begun his first year in a secular kindergarten where xmas is celebrated. We however do not celebrate it at home at all. Do you think I am doing right? Instead of xmas, I think Hanuka would be a better alternative, but my question is: are we allowed to celebrate it? And can we even say directly that xmas is forbidden for Torah observant Noahides?

You are allowed to celebrate chanukka by rejoicing in the preservation of the Torah achieved by the victory G-d gave the Maccabees. Adopt customs that express for you a sense of joy. Since Christmas celebrates the birth of someone many gentiles have accepted as a god, ideally you should not participate in this as idolatry is one of the seven Noachide laws.