Shabbat and Holidays

We forgot to plug in our hot plate, and so we asked our child (9 years old) to plug it in 11 minutes after sunset. We second-guessed ourselves in the morning. Was it permitted? If not, could we have used the hot plate then and benefitted from the food that was on it?

I am a man living alone. Last week, I forgot to light Shabbat candles. Must I light an extra one from now on?

Why do we say "Pnei Shabbat Nekabela"? What does the Shabbos have to do with the face?

May I pull teeth on Shabbos? Does clipping fingernails on Shabbos involve a Torah prohibition? On Yom Tov, may I dig up earth to perform the mitzvah of kisuy hadam?

We like to keep our challot in a warm place until bringing them to the table after Netilat Yadayim so they taste their best. Must they be on the table during Kiddush?