What is the Islamic ruling on the aqiqa?
All praise is due to Allah, and may peace and blessings be upon our Master, the Messenger of Allah.
The 'aqīqah is a confirmed Sunnah (sunnah mu'akkadah). Two sheep are to be slaughtered for a newborn boy, and one sheep for a newborn girl. This is established by numerous Prophetic traditions, among them:
The narration of Samurah ibn Jundub, may Allah be pleased with him, who reported that the Messenger of Allah ﷺ said: "Every child is held in pledge for his 'aqīqah, which is slaughtered on his behalf on the seventh day, and he is named, and his head is shaved." — Narrated by al-Tirmidhī, who graded it as ḥasan ṣaḥīḥ.
And the narration of 'Ā'ishah, may Allah be pleased with her, who said: "The Messenger of Allah ﷺ commanded us to slaughter one sheep as 'aqīqah for a girl, and two sheep for a boy." — Narrated by Aḥmad and Ibn Mājah.
The imperative in these narrations is understood to denote recommendation rather than obligation, based on the ḥadīth of 'Amr ibn Shu'ayb, on the authority of his father, on the authority of his grandfather, who said: The Messenger of Allah ﷺ was asked about the 'aqīqah, whereupon he said: "Allah does not love 'uqūq" — as though he disliked the name itself — and then said: "Whoever has a child born to him and wishes to offer a sacrifice on their behalf, let them do so: two equivalent sheep for a boy, and one sheep for a girl." — Narrated by Aḥmad and Abū Dāwūd.
The legal inference drawn from this narration is that the Prophet ﷺ linked the slaughter to the wish and willingness of the individual, saying: "whoever wishes to offer a sacrifice... let them do so" — thereby indicating that the 'aqīqah is recommended (mustaḥabb) and not obligatory (wājib).
And Allah Almighty knows best.
What is required of a traveler or a sick person if they broke their fast and then their excuse ceased?
If a traveler settles or a sick person recovers after having broken their fast, it is recommended for them to refrain from eating and drinking for the rest of the day, but it is not obligatory.
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 to pay the Fitr Zakah (obligatory charity) of Ramadan on behalf of a dead person?
The Fitr Zakah of Ramadhaan isn`t due on one who had passed away before the sunset of the last day of Ramadan. And Allah Knows Best.