Should an unmarried woman light one or two Shabbat candles? I have seen both practices, but it seems that only little girls light one candle and that a grown-up woman lights two although she is not married. (I light two following the logic of "shamor and zachor".) I know a married woman lights two.
With candles, their's a large variety of customs, so this is only a partial answer.
Until marriage, girls light one candle.
This is from the lubavitcher Rebbe. Unfortunately, I can't find the exact source of the article, but I heard the Rebbe said to do it that way to make a distinction between the lighting of an unmarried person and a married person.
The most common custom is that there is no special duty for a single girl to light Shabbos lights at all. If anyone but the married woman of the house is lighting, the tradition is to light two. Including if a wife isn't home and the husband is lighting. Or your case.
The Lubavitcher rebbe invented the practice of all girls lighting. It hasn't been going on long enough to be qualify as a "minhag", yet. Rabbi JB Soloveitchik advised families that knew their family minhag not to leave their minhag.
As for making a berakhah, for Sepharadim -- the Shulchan Arukh (OC 263:8) would not let someone who is adding light to a room that is already lit make a berakhah. For example, if two families are sharing a dining room, the second person to light shouldn't make a berakhah. So the mother would have to light first, and then the daughter would light without a berakhah. For Ashkenazim -- the Rama disagrees, and allows a berakhah when lighting additional lamps in an already lit room. So, the daughter can make a berakhah in this situation.
(Side note: ideally, one should turn on the electric lights in the dining room as well, so that one is making a berakhah on the lights actually being used for the meal. But because of the above, an Ashkenazi can make a berakhah on the Shabbos candles either way, it's just less than ideal to only make the berakhah on the additional light and not the primary light source.)
Others raised the topic of how many lights should be lit when it's the wife or someone else lighting for an entire household: two, or the minhag of one per person, possibly plus a "fine" of one for each week missed until now.
If you do not know your minhag, I would advocate for just lighting for Shamor and Zakhor. I would like to see the other custom disappear entirely, frankly. I think of the childless wife who passes by the window seeing 8, 9, 13 candles, and feeling pain. Or the mother who lost one of her children, who starts her Shabbos with a sad reminder.