2. On Erev Shabbos, the Chanukah lights are kindled before the Shabbos candles even if a man is lighting the Shabbos candles. The reason is that there is a view which holds that men are mekabel Shabbos when he lights the Shabbos candles and melacha is prohibited. Although most poskim disagree with this view, and feel that men are not mekabel Shabbos when lighting the Shabbos candles, the custom is to preferably conduct himself accordingly.

3. However, if a man lit the Shabbos candles and did not intend to usher in Shabbos, he may kindle the Chanukah lights afterwards. This Halacha concerns a man, who does not accept Shabbos by lighting the Shabbos candles. However, when a woman lights the Shabbos candles, the custom that the she does accept Shabbos and is prohibited from doing any melacha. Therefore, if she should, accidentally, light the Shabbos candles, she is no longer permitted to kindle the Chanukah lights. She should, instead, instruct another person to light for her (as long as it is before sunset) and recite the blessing “Lehadlik Ner Shel Chanuka” on her behalf. She may, however, recite “Sheasa Nissim”. (Mishnah Berurah 679:1)

4. The poskim debate whether one should light the Chanukah lights before reciting Havdalah this Motzei Shabbos, or is Havdalah recited before kindling the Chanukah lights. (See Shulchan Aruch, Rama, Mishnah Berurah and Biur Halacha 681 for full discussion) In shul, the custom is to light Chanukah lights first. At home, however, since there is basis for both views, one should continue to conduct himself according to his own custom. If one has no specific custom he should perform Havdalah first and then kindle the Chanukah lights. (Opinion of Harav Yosef Eliyahu Henkin zt”l cited in Luach and of Harav Shimon Eider zt”l in Halachos of Chanukah page 44)