Sam2:
The Shulchan Aruch in Orach Chaim 678:1 says that ner shabbos supersedes ner chanukah and although the Magen Avraham says that perhaps nowadays since we light inside, ner chanuka is better, the Mishnah Berura does not accept the Magen Avraham’s position and the Aruch Hashulchan says you can rely on it in a sha’as hadchak. The Shulchan Aruch in 263:3 says that ner shabbos supersedes wine for kiddush. And back in 678:1 he says that ner Chanukah comes before kiddush. But this is all if you have bread. If you don’t have bread, it’s a machlokes acharonim about bread vs ner chanukah. Both the Mishnah Berura and the Aruch Hashulchan pasken that bread supersedes ner chanukah, and the commentaries say that bread even supersedes ner shabbos. In my case, the mohel won’t do the bris until you give him the money.
Regarding the bet, I think that DaasYochid would say that ther’s an anan sahadi that the friend knows he’s wrong (this would be a good place for an emoticon).
And let’s say the case is that the kohen(im) and the mohel are leaving town right after Shabbos and they’re not coming back.