The Gemara concludes that the bracha is להדליק candles of Chanukah bc the lighting is the mitzvah and therefore if a child lit the menorah the mitzvah would not be fulfilled.

Women are obligated in Chanukah lights bc they were part of the miracle

Even a guest needs to light Chanukah candles. They can also use option of contributing a little money for the oil. In addition, if someone is lighting in their primary home, that exempts them.

Olive oil is the choicest for ner Chanukah. It is also the choicest oil used to produce black ink.

Someone who sees Chanukah lights should make שעשה ניסים (and שהחינו on the 1st night) if they won’t be lighting a menorah for whatever reasons

We keep שעשה נסים for each of the days of Chanukah bc each day was a new miracle

We say וצונו on lighting menorah even though it’s not from the Torah bc the Torah says we have to listen to the Rabanan. But there’s no bracha on separating demai bc demai is either a safek to begin with or only due to a minor concern that. There is a bracha on 2nd day Yom tov even though it’s a safek so ppl take will take it seriously.

A person with two entrances from two dif directions must light two menoras so ppl don’t suspect him of not lighting a menorah. We learn this concept form פאה where the Torah says to leave the corner of the harvest and not just designate any part of the harvest for the poor so ppl won’t suspect the farmer of not fulfilling peah.

A lamp with two seperate wicks can be used for two people’s mitzvah. But if the wicks will come together it is not kosher even for one person bc it resembles a torch which is not acceptable for menorah.

A person with enough money for either Shabbos candles or Chanukah lights should spend it on Shabbos candles bc of שלום בית. Chanukah candles should have priority over buying wine for kiddush bc of פרסומי ניסא.

Reward for lighting Shabbos and menorah candles is having sons who will be torah scholars.

The right time for Shabbos candles is not too early before Shabbos (it’s not apparent that the candles are for Shabbos) but also not right before. We learn this from the pillar of fire in the desert that overlapped a bit with the cloud during the day before the day ended.

We don’t use שמן שריפה for Shabbos candles. This is oil of Terumah that became tamei. It shouldn’t be used either bc one may tilt the oil out of zealousness to do the mitzvah of burning the oil or really it is only forbidden when Erev Shabbos is also a Yom tov bc there is a law that one cannot burn disqualified kodshim on Yom tov. (It is burning not for אוכל נפש)