Candle Lighting Questions and Answers

The rabbi in my synagogue tells me that my daughter should begin lighting Shabbat candles. My very traditional grandmother disagrees. Can you please enlighten me?

I know that we light holiday candles on the first two nights of Passover. But what happens when the first day of Passover falls on Shabbat, and the second night of Passover begins on Saturday? Does that change things with the lighting on Saturday night?