[Avodah] chanukah candles and women

[Eli Turkel]

I still do not understand why wives generally do not light chanukah candles
according to the Ashkenazi custom that each person lights seperately

1. Is there any other mirzva where we apply ishto kegufo?
Certainly a woman can shake a lulav with a beracha (Ramah) even though
her husband already did it

2. If ishto kegufo why can;t the wife light even lechachtila for the husband and
why if he is absent does he need to appoint her as a shaliach?

3. According to Rambam that mehadrin min hamehadrin means the
husband/father lights for each member of the family (not like the Ramah that
each lights for themselves) does the husband add candles for the wife?

4. Why dont single girls (over 12) at home light chanukah candles.
They are now required
and one cant apply ishto kegufo. The fact that they wont light when married
doesnt override the present mitzvah (it is not just chinuch she is over 12)

I understand that by RYBS the women in the house did light but that is
not the general custom

-- 
Eli Turkel