If a woman becomes pure from menstruation before the Fajr Adhan in Ramadan, is she required to fast?
If a woman becomes pure (from menstrual period) before the Fajr Adhan, she must fast, as the impediment preventing her from fasting has been removed. The Sharia maxim in this regard states: "When the impediment is removed, the obligation returns."
She should then make the intention to fast before Fajr and perform ghusl (ritual purification) for prayer, whether before or after Fajr.
What is the ruling on one who vowed not to speak to a certain person, then forgot his vow and spoke to him?
All praise is due to Allah, and peace and blessings be upon our master, the Messenger of Allah.
Whoever swears an oath or makes a vow to abstain from something has a choice: if he wishes, he may keep to his vow, or if he wishes, he may offer the expiation of an oath (kaffārat yamīn). The Prophet (peace and blessings be upon him) said: “The expiation for a vow is the expiation for an oath.” Narrated by Muslim. This type of vow is called a nadhr al-lajāj (a vow made in stubbornness or anger).
If a person makes a vow and then forgets it, nothing is due from him, for forgetfulness is among the excuses that lift legal responsibility (taklīf) from a Muslim. This is based on the saying of the Prophet (peace and blessings be upon him): “Actions are judged only by intentions, and every person will have only what he intended.” [Narrated by al-Bukhārī]. There is no intention for the one who forgets or errs. It is also based on the report: “Indeed, Allah has pardoned for my Ummah mistakes, forgetfulness, and what they are compelled to do.” Narrated by Ibn Mājah and others, and graded authentic by Ibn Ḥibbān and al-Ḥākim.
It is stated in ʿUmdat al-Sālik (p. 243), one of the books of the Shāfiʿī school: “Whoever swears, [for example], ‘I will not enter the house,’ and then enters it forgetfully, ignorantly, under compulsion, or being carried, he does not break his oath.” And Allah Almighty knows best.
Is it permissible for a person to give the Zakah (obligatory charity) to his daughter-in-law?
Yes, it is permissible for a person to give the Zakah to his daughter-in-law if she was poor, and none provided for particularly by whom are obliged to provide for her. And Allah Knows Best.
What should a person who doubted having missed a pillar of prayer do?
All praise be to Allah, The Lord of The Worlds. The prayer of one who doubts having missed one of its pillars is valid, and nothing is due on him/her since having a doubt after offering the act of worship doesn`t undermine its validity. And Allah Knows Best.