Does the emission of pre-seminal fluid (madhy) after Tarawih prayer invalidate the fast and necessitate ghusl and making up the days in which one did not perform ghusl?

Your fast is valid if pre-seminal fluid (madhy) is discharged at night. However, if it is discharged during the day, the fast is not invalidated by its emission, and ghusl (ritual bathing) is not required for the discharge of madhy. Rather, what is required is istinja' (washing the private parts), washing whatever it stained on clothes, and wudu' (ablution). It is not permissible to establish a friendship with a non-mahram woman because it is among the abominable acts that could lead to committing zina (unlawful sexual intercourse). Allah Almighty says: "O you who have believed, do not follow the footsteps of Satan. And whoever follows the footsteps of Satan - indeed, he enjoins immorality and wrongdoing." The matter becomes even worse if this occurs during Ramadan.