Does the expiation for an oath become obligatory for someone who vowed to God to abandon a sin, then fell into it? And what is the ruling for someone who forbids herself from eating and drinking in her parents' home while she is unmarried and living with them?

A Muslim must avoid sins. If someone makes a covenant with Allah to abandon a sin or perform an obligation, and then violates that covenant, the majority of scholars hold that there is no expiation for them because that was originally an obligation, and a vow cannot be made for something already obligatory. However, Shaykh al-Islam and some verifying scholars are of the opinion that an expiation for breaking an oath is due.

Therefore, the sister must adhere to abandoning the sin, and if she returns to it, she must offer expiation for what she covenanted with Allah, according to the view of Shaykh al-Islam and those who agreed with him.

As for forbidding eating and drinking from her family's house, that is idle talk and does not prohibit what Allah has made lawful.