What is the ruling on performing dry ablution (tayammum) on a wall or stone?
One of the conditions for tayammum is that it be with pure, clean dust (soil). It is not valid to perform tayammum by striking stones, a wall, sand that has no dust (i.e., that does not produce dust), pebbles alone, or clay, as these are not from the earth or its same category. And Allah the 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.
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.
Someone wiped over his shoes after wearing them in a state of purity, then took them off and prayed without them?
Ablution is not invalidated by taking off leather socks or shoes after wiping over them. However, whoever takes them off after wiping must wash his feet only. If he prayed without washing his feet, he must wash his feet and repeat the prayer. And Allah the Almighty knows best.