Is a woman's fast valid if she purifies from menstruation after Fajr, and is her intention to fast sufficient, and is she sinful for not verifying purity before Fajr?

For the fast of Ramadan (definition), it is a condition to make the intention at night, based on the Prophet's (peace be upon him) saying: "Whoever does not make the intention to fast from the night, then there is no fast for him." Accordingly, fasting with a wavering intention is not sufficient and requires making up the day.

As for ghusl (definition) (ritual bath) after menstruation, it is obligatory for a woman to perform ghusl immediately upon seeing purity and not delay it. However, some scholars permit delaying ghusl for half a day or a day to ensure complete purity, especially if she sees dryness but not the white discharge (al-qassah al-bayda'), as a means of facilitation and to avoid hardship.

It is sufficient for a menstruating woman to make her intention from the night if it is her habit to attain purity, and she makes a firm intention from the night. If she checks for purity before going to sleep, she is not required to check again before dawn.