Does a woman's fast become invalid if water enters her private parts during istinja' (washing after urinating or defecating), and how should she perform istinja' to wash away mathy (pre-ejaculatory fluid) without introducing water into her private parts?

The nullifiers of fasting are called "mufattirat" and they are: Intercourse, and intentional eating and drinking; as Allah Almighty says: "So now have sexual relations with them and seek what Allah has ordained for you, and eat and drink until the white thread of dawn becomes distinct to you from the black thread [of night]. Then complete the fast until the night." Ejaculation due to lust; as the Prophet, peace and blessings be upon him, said: "The fasting person leaves his food, drink, and desires for My sake." Nutrient injections that substitute for food and drink. Intentional vomiting; as the Prophet, peace and blessings be upon him, said: "Whoever vomits intentionally while fasting must make up for it, but whoever is overcome by vomiting is not required to make up for it." The exit of menstrual or postpartum blood; as the Prophet, peace and blessings be upon him, said: "Is it not true that when she menstruates, she neither prays nor fasts?" And the scholars have unanimously agreed that the fast of a menstruating or postpartum woman is not valid.

As for a woman's istinja' (washing after defecation or urination), it does not nullify the fast, as the water does not reach her internal cavity and it does not involve the meaning of eating or drinking.