A woman became pure [from menstruation] before Fajr, but did not perform ghusl until after sunrise — what is the ruling on her fast?
All praise is due to Allah, and peace and blessings be upon our master, the Messenger of Allah ﷺ.
Her fast is valid, since ghusl (ritual bathing) is not a condition for the validity of the fast, but rather for the validity of the prayer. However, she is sinful for delaying the Fajr prayer beyond its designated time without a valid excuse.
It is known that the time for Fajr prayer ends at sunrise. Nevertheless, she must still perform ghusl, and make up the Fajr prayer. And Allah, the Exalted, knows best.
Is washing the private part after urinating (Istinjaa`) a condition, and is it done with water and soap, or with water only?
Istinjaa` is obligatory for removing impurity, and it can be done with toilet paper, or a stone, or water. It is preferable to do Istinjaa` first with paper, or stone, or the like, then to wash the private part with water until making sure that the impurity has been removed. Using soap is not a condition, but there is no harm in doing so provided that it is washed off with water. It is also permissible to use either water, or paper if impurity is removed by any.
Is a person who forgot to make up missed fasts until the next Ramadan began required to pay expiatory compensation (Fidyah) alongside the makeup fast (Qada')?
All praise is due to Allah, and peace and blessings be upon our master, the Messenger of Allah.
Whoever forgets to make up missed fasts of Ramadan (Qada') until the following Ramadan begins incurs no sin, pursuant to the statement of the Messenger of Allah (peace and blessings be upon him): "Indeed, Allah has pardoned for my nation their mistakes, their forgetfulness, and that which they are coerced into doing." [Narrated by Ibn Majah, and Al-Bayhaqi in Al-Sunan Al-Kubra]
Furthermore, such an individual is not obligated to pay a expiatory compensation (Fidyah). It is stated in Bushra Al-Karim (p. 580)—one of the authoritative Shafi'i jurisprudential texts: "As for delaying it [the makeup fasts] due to a valid excuse—such as travel, breastfeeding, forgetfulness, or ignorance of the prohibition of delay (even for one living among scholars)—no Fidyah is required. This is because delaying performance during the actual month is permissible due to these excuses; hence, delaying makeup fasts is even more permissible, even if it continues for years."
And Allah Almighty knows best.
Can a menstruating woman listen to the Quran from the radio or television?
Yes, a menstruating woman is allowed to listen to the Quran from the radio or television. What is forbidden for her is reciting the Quran and touching the Mus-haf, but listening is permissible—in fact, it is an act of worship.However, she should not repeat along with the Qur’an or try to keep pace with it.