Is the man's fluid that exits a woman after intercourse considered impure, and does it necessitate redoing ablution, or is it sufficient to wash the private parts, and if it exits during prayer, is it necessary to redo ablution for the obligatory prayer?

The semen of a man is pure, according to the more preponderant opinion. Its exit from a woman's private parts after intercourse and ritual bathing (ghusl) nullifies ablution (wudu), provided it entered through sexual intercourse, according to the Maliki school. Likewise, all secretions exiting the private parts nullify ablution. If any of these exit during prayer, the ablution is nullified, the prayer becomes invalid, and a new ablution is required.