The obligation of lighting the Chanukah candles:
The head of each household is obligated to light candles for Chanukah in his home. This law applies both for men and women. One who lives off charity is nevertheless obligated to light candles, and must go to the extent of either borrowing money or selling his clothes in order to buy them.
Single Women: A single, divorced, or widowed woman is obligated to light Chanukah candles in her home.
Other household members: The additional household members who live and are supported by the head of the house are not obligated to light the candles. Furthermore, according to some Poskim they are specifically not to do so, and so is the Sephardic custom. However other Poskim rule that [although from the letter of the law there is no obligation for other household members to light], nevertheless each and every household member is [obligated] to light individual candles [due to an age honored custom of Mehadrin] and so is the Ashkenazi custom.
Wives and daughters: Despite the above Ashkenazi custom for all household members to light, nevertheless regarding wives and daughters the custom is for them to follow the letter of the law and fulfill their obligation through their husband/father, and not to light their own Menorah. Regarding children see below.
What does the wife do if her husband is not in town? If the husband/father is away from home the wife is obligated to light the Chanukah candles at home with a blessing. Likewise if the wife is away from home she is to follow the same law as a male married guest as brought in Halacha 4A.
Children below age of Mitzvos: Male children only begin lighting the Chanukah lights some time before their bar-mitzvah.Nevertheless in many families even very young children are educated to light on their own.
If a child is living on his own must he light? If a child is living on his own then he’s obligated to light the Chanukah candles starting from the age of Chinuch, which is the age that the child understands the Mitzvah of lighting Chanukah candles.
According to Sefaradim, is a married couple who is still living by her or his parents to light the candles separately?
If an Ashkenazi is living by a Sefardi how many candles is he to light?
He is to light following his custom. The Sefardi landlord may not protest.
Must household members who are fulfilling the Mitzvah with the father of the house be present at the time of the blessing?
Seemingly not, as the Mitzvah is fulfilled with one Menorah per household. However, it requires further analysis regarding if those members who did not hear the blessings should recite “She’asah Nissim” upon seeing the Menorah.
 The reason why women are obligated despite the Mitzvah being one that is caused by an arrival of time in which case women are usually exempt from, is because the women were actively part of the Chanukah miracle. [Kol Bo]
 671/1; 675/3
 Such as children, above and below Bar Mitzvah, which live at home; one’s wife; an orphan which one was taken into one’s home.
 Michaber 571/2; Tosafus Shabbos 21b; the recorded custom of Spain brought by Rambam 4/3, even though the Rambam is the source of the second opinion.
 Michaber 571/2 as rules Tosafus Shabbos 21b, and as is the recorded custom of Spain brought by Rambam 4/3, even though the Rambam is the source of the second opinion.
 Rama 571/2; Rambam 4/1-2
 Rama 571/2 as rules Rambam 4/1-2; The Bach writes that this is the followed custom of all communities with exception to Spain. The Bach concludes that one whose custom is like Tosafus is not to swerve from it. Darkei Moshe explains that today being we all light inside and there is no longer confusion as to how many candles one has lit, even according to Tosafus one is to follow the ruling of the Rambam. See Shaareiy Hamoadim Chanukah 39
 Sefer Haminhagim p. 157 [English]; M”B 671/9 and 675/9
Reasons mentioned: 1) One’s wife is like his body and it is thus considered as if she lit the candles, and is improper for daughters to light when mother is not lighting. 2) Women are not expert in the blessings.
 Sefer Haminhagim p. 157 [English]
Other Opinions: According to Rama [675/3] once a child reaches the age of Chinuch he is obligated to light. The M”B 675/14 brings opinions that argue on Rama and hold that even according to the Ashkenazi custom that all male household members light, nevertheless there’s no obligation to educate a child in a matter of Hidur Mitzvah, and therefore he is not obligated to light. This is seemingly the opinion held in Sefer Haminhagim. According to Michaber obviously the child does not light being that according to him only one person lights in each home.
 Shevach Hamoadim p.101
 Taamei Haminhagim 848
 Shaareiy Teshuvah 671
 See Michaber 676/3 which contradicts 677/3; M”B 676/14; Piskeiy Teshuvos 675/3; Ashel Avraham Tinyan 675 writes even a girl over chinuch who did not hear the blessing must say it upon seeing the candles.