I am only answering this part:
Is there any expiation for the sin of illicit sex?
Various Dharmashastras declare various expiation for illicit sex. I am quoting some of them as below:
Gautama (23.12, 13, 32).—‘The guilt of one who has intercourse with the wife of a friend, a sister, a female belonging to the same family, the wife of a pupil, a daughter-in-law,—or with a cow—is as great as that of him who violates the Guru’s bed. Some people declare the guilt of such a person to be equal to that of a Student who breaks the vow of continence. For intercourse with a female of one of the lowest castes, one shall perform a Kṛcchra penance during one year.’
Baudhāyana (2.2.13-14).—‘Intercourse with females who must not be approached, cohabitation with the female friend of a female Guru, with the female friend of a male Guru, with an Apapātra woman, or with a female outcast,......... the expiation is to live like an outcast for two years.’
Vaśiṣṭha (20.15-16).—‘The expiation for intercourse with the wife of a teacher, of a son, or of a pupil is that, having shaved all his hair and smeared his body with clarified butter, the man shall embrace the heated iron-image of a woman. If he has had intercourse with a female considered venerable in the family, with a female friend, with the female friend of a Guru, with an Apapātra female, or with an outcast,—he shall perform the Kṛcchra penance for three months.’
Viṣṇu (53.1)—‘One who has had illicit sexual intercourse must perform the Prājāpatya penance for one year,—according to the rule of the Mahāvrata, clad in a garment of bark and living in a forest.’
But if one repents for his bad Karma and devoted oneself to their adorable lord all sins will be cleansed, there is no doubt. This is mentioned in Vishnu Purana, Book 2, Chapter 6.
Let any one who repents of the sin of which he may have been culpable have recourse to this best of all expiations, remembrance of Hari: by addressing his thoughts to Náráyańa at dawn, at night, at sunset, and midday, a man shall be quickly cleansed from all guilt: the whole heap of worldly sorrows is dispersed by meditating on Hari; and his worshipper, looking upon heavenly fruition as an impediment to felicity, obtains final emancipation.