The Halacha requires lighting candles in honor of Shabbat and Yom Tob with the appropriate Beracha. This is clearly codified in the Shulhan Aruch in Siman 263. However, Maran states that Yom Kippur is different and the custom is to light without a Beracha.
This issue is rooted in a Machloket Rishonim (dispute between the early authorities) between the Mordechi and the Rosh. The Rosh holds that candles should be lit, as this prevents intimacy; one is not allowed to have relations in the light. On the other hand, the Mordechi maintains that lighting candles will enable the husband to gaze at his wife and become attracted to her, and therefore candles should not be lit.
In Hilchot Yom Kippur (610), Maran cites only the opinion of the Rosh that one should light with a Beracha. This is the opinion of Ben Ish Hai and the Kaf HaHaim, as well as many other Poskim, including the Rema, Rabbi Zalman, Pri Megadim and Hayeh Adam.
However, other Poskim, such as Rabbi Haim Palachi, the Peri Hadash and the Aruch Hashulhan hold that since there is a difference of opinion, Safek Berachot L’Hakel (a Beracha should not be recited in a case of a doubt) and therefore, one should not recite a Beracha when lighting. Hacham Ovadia overrules this claim, saying that where there is an established custom, the principle of Safek Berachot L’Hakel does not apply. Indeed most communities do have the custom and light with a Beracha.
The custom of Halab was specifically not to make a Beracha on the candles of Yom Kippur. In fact, half the city of Aleppo did not even light candles on Yom Kippur, as testified by Hacham Yishak Zafrani in his Derech Ere"s, and Hacham Yishak Shehebar of Argentina. The Kol Ya’akob Weekday Siddur also records the custom of Halab as not to recite the Beracha.
When Yom Kippur falls on Shabbat, Maran rules that all opinions concur that candles are lit with a Beracha. Nevertheless, there is still a question with regard to the custom of Halab. Hacham Eliyahu Hamway wrote that even in such a case, a Beracha should not be recited because of Safek Berachot L’Hakel. Yet, after surveying the various authorities, it seems that the custom in America today is to light candles with a Beracha on Shabbat and Yom Kippur.
The beracha of Shehecheyanu is recited in Shul after Kol Nidre. It is not a Beracha on the Kol Nidre, but on the holy day itself. Therefore, if a woman attends Shul, she should recite it then. If not, she should recite it at home, either when lighting the candles or praying Arbit.
Most communities light candles for Yom Kippur with a Beracha. The custom of Halab is not to recite a Beracha, and some do not even light at all. However, when Yom Kippur falls on Shabbat, all agree that a Beracha is recited.