Is it a sin to caress one's husband and for him to insert part of his organ into the vagina without seeing purity and performing ghusl during the last days of the menstrual period, and what must be done to expiate this?

The spouses must repent to Allah Almighty for engaging in intercourse before the cessation of menstruation and performing ghusl (definition) (ritual bath) after it. Even if the bleeding stops and the sign of purity is observed, intercourse is not permissible before performing ghusl. Ibn Qudamah narrated the consensus (ijma') on the prohibition of cohabiting with a menstruating woman before ghusl, citing the Almighty's words: "And do not approach them until they are pure. But when they have purified themselves, then come to them from where Allah has ordained for you." The verse stipulates two conditions for permissibility: the cessation of bleeding and performing ghusl.