Is it valid to fast the last day of the Six Days of Shawwal, and does she have to make up for it if she broke her fast on a day she was supposed to be making up, and how can she expiate for that?

Fasting on Saturday is valid. Eating after sunset is not a condition for the validity of the fast. The fasting person is considered to have broken their fast as soon as the sun sets, based on the Prophet's (peace be upon him) saying: "When the night approaches and the day retreats and the sun sets, then the fasting person has broken their fast." As for fasting on Sunday, it is not valid unless the intention is made for it from the night before. If you intend to fast it and you experience hardship and difficulty, there is no sin in breaking your fast.