What is a single girl’s obligations in candle lighting? Is it the same as a man’s? What would it include- in regards to eating before lighting or not, appointing a shomer if you will be lighting late, and may one have others in mind when lighting?
Are the obligations the same for a single girl who is not married yet and for an older woman who was once married?
A single girl [whether once married or not] is fully obligated in lighting Chanuka Neiros as a man, as such all the relevant halachos you mention would apply. The only exception is a single girl who is in her parents home, where many have the custom for her to fulfill her obligation with the lighting of her father.
Two people living together can fulfill their obligation with one Menora, but not by merely having one another in mind, rather they must share ownership of the oil/candles. A girl who is visiting by lighting time but has her own home can not fulfill her obligation there and must light on her own when returning that night.