Does a child have to do their own Hadlokos Neiros (candle lighting) for Shabbos or Yom Tov if their mother is in a different time zone, or can the mother still light for the child?
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The semminary Rabbanim as a general rule in Eretz Yisrael forbid the girls from lighting their own neirot, claiming that their parents light for them(exception being Mayyanot and Lubavitcher Sem). Claiming that a girl only lights when she is is married.
While I personally have never understood the exact logic behind their rulings considering Rabbanim like R' Eliyashiv and R' Shmuel Auerbach rule that way(according to the people who go to sems they oversee) I assume there is a valid halakhic reasoning behind it.
According to Sephardi halakha a woman lights for her own home and the woman of the house alone is permitted to say the beracha(The Hida Mihazik Berakha (O.H. 263:4) and Shoel V’Nishal (2, 58), Kitzur Shulkhan Arukh of HaRav Rafael Barukh Toledano (134:27), Sefer Ben Ish Hai(Year 2 Parashat Noah) Kaf HaHaim(OH 263:34), Ohr L’Tzion (Vol. 2, 18:3, there are others as well but that pretty much sums up most of the major ones). They do permit a visitor to light in her own room with a berakha.
Rabbi Ovadia Yosef initially challenged this ruling(Yabia Omer 2 OH 16 and Yehaveh Da'at 2:33). Essentially he ruled that since this was based on the Kabbalah of the Arizal and since Kabbalah is not ikar Hadin, that a girl should begin to light at the age of 3 with a berakha. A view that was also later adopted by the late Lubavitcher Rebbe.
However, he faced such a firestorm from Rabbanim such as the Baba Sali(as well as some of the Gedolim listed above) that he finally withdrew his pasak.
All of that to say if there is a Ba'ala Bayit there an unmarried woman should not light on her own.
So it would seem that for the most part the answer to the overall question is no.
You must do your own hadlakos neiros with a bracha if you are living next door. Every house must have light and you make a bracha on the light. The woman is charged with her own house for kabbalistic reasons (woman extinguished the light of the world- Adam...) S.A. O.C. 263:2-3, 5-6