What is the ruling on one who wiped over his leather socks (*khuff*) while resident and then traveled, or wiped while traveling and then became resident? And likewise, what is the ruling on one who incurred a minor ritual impurity (*ḥadath aṣghar*) while resident, then traveled and wiped while traveling?
All praise is due to Allah, and peace and blessings be upon our master, the Messenger of Allah.
Whoever wipes over his leather socks (khuffayn) while resident and then travels, or wipes while traveling and then becomes resident, before a day and a night have passed in both cases, completes the wiping period of a resident. If he wipes while resident and then travels after a day and a night have passed, he must remove the socks, because the period has ended. Likewise, if he wipes while traveling and then becomes resident after a day and a night have passed, he must remove them as well.
Whoever breaks his wuḍūʾ while resident and then wipes while traveling takes the ruling of a traveler as regards the duration of wiping, so long as he does not become resident. It is stated in ʿUmdat al-Sālik wa ʿUddat al-Nāsik (Vol.1/p.15): “If he wipes over both [socks] or one of them while resident and then travels, or wipes while traveling and then becomes resident, or doubts whether he began the wiping while traveling or while resident, he completes only the wiping period of a resident. But if he broke his wuḍūʾ while resident and wiped while traveling, he completes the period of a traveler, whether or not the full time of a prayer had passed over him while resident.” And Allah Almighty knows best.
Is the son of the sister by breastfeeding considered a mahram in Islam, and is it permissible for a woman to go for Hajj with him?
Everything that is prohibited by lineage is also prohibited by breastfeeding. The son of the sister by breastfeeding is considered a mahram, just like the son of the sister by blood, and it is permissible for him to be her mahram for Hajj and Umrah. And Allah Knows Best.
Does the intention (niyyah) of the principal (muwakkil) suffice for the sacrifice (dhabḥ) of the udhiyyah?
Praise be to Allah, and peace and blessings upon our master, the Messenger of Allah.
If a person appoints an agent (wakīl) to perform the slaughter (dhabḥ) on their behalf, the intention (niyyah) of the principal (the one appointing the agent) suffices, and there is no need for the agent to have this intention himself. In fact, even if the agent is unaware that he is performing the sacrifice on someone's behalf as an udhiyyah (sacrificial offering), this does not affect its validity. And Allah, the Most High, knows best.
What should the one performing the slaughter say at the time of slaughtering the 'aqīqah?
All praise is due to Allah, and may peace and blessings be upon our Master, the Messenger of Allah.
It is Sunnah to say the following supplication at the time of slaughtering the 'aqīqah:
"Bismillāhi wallāhu Akbar, Allāhumma laka wa ilayka, hādhihi 'aqīqatu fulān."
("In the name of Allah, and Allah is the Greatest. O Allah, this is for You and unto You — this is the 'aqīqah of [the child's name].")
This is based on what al-Bayhaqī narrated in Al-Sunan al-Kubrā (Vol.9/P.511), that the Prophet ﷺ said: "Slaughter it in his name and say: In the name of Allah, and Allah is the Greatest. O Allah, this is for You and unto You — this is the 'aqīqah of so-and-so."
And Allah Almighty knows best.