Hadlakas Menorah on Erev Shabbos

My good friend R'Chaim Brown has a post about hadlakas menorah on Erev Shabbos as viewed through the lens of tadir v'sh'eino tadir.
I would like to look at it through a different angle.

Here are a few questions.

1) We pasken that Ner Chanukah is before Ner Shabbos. Why don't we say that the woman of the house should first light Ner Shabbos and tehn the husband can light Ner Chanukah since the husband is not m'kabeil Shabbos when his wife lights Shabbos candles. Also, a woman who lights Shabbos candles can ask her husband to do melacha for her.

2) When we light candles Erev Shabbos before Sh'kiah is that considered the z'man hadlakah? If it is not the z'man hadlaka and we only light before sh'kiah because ein berierah then how does this work since we hold hadlaka oseh mitzva. We are lighting before the z'man chiyuv and we l'chorah didn't do a proper hadlakah.

I don'thave time to answer these questions now but here are a few mareh mekomos to chew on.

1) Siman 679 and nosei keilim there
2) Siman 673:2 and the Taz in 673:2
3) The Ran and Shitas B'Hag on the sugyah of kavsa ein zakuk lah
4) Terumas HaDeshen Siman 102
5) Shut Pri Yitzchak Chelk 2 Siman 8