Is it permissible for a woman to shake hands with her brother-in-law?
It is forbidden for the woman to shake hands with her brother-in-law because he isn`t a Mahram (unmarriageable) of hers.
Does the clipping of nails nullify ablution?
No, it does not, and it is preferable to wash the hands afterwards.
Who is the one deemed "able" (al-qādir), for whom the uḍḥiyah (sacrificial offering) is sunnah?
All praise is due to Allah, and peace and blessings be upon our master, the Messenger of Allah ﷺ.
The one who is deemed "able" (al-qādir) [to perform the uḍḥiyah, i.e., the sacrifice] is someone who possesses wealth sufficient to acquire the sacrificial animal, over and above what is needed to cover his own living expenses and the living expenses of his wife and children — or of anyone else whose financial support (nafaqah) is legally obligatory upon him — for the day of ‘Eid and the three days of Tashrīq [that follow it], since this is the designated time period for the sacrifice. And Allah, the Exalted, knows best.
What is the ruling on the prayer of one who said "Subḥāna Rabbiya al-ʿAẓīm" in prostration (*sujūd*) and forgot to correct it?
All praise is due to Allah, and peace and blessings be upon our master, the Messenger of Allah.
Saying “Subḥāna Rabbiya al-ʿAẓīm” in bowing (rukūʿ) and “Subḥāna Rabbiya al-Aʿlā” in prostration (sujūd) is one of the hayʾāt (non-essential sunnahs) of the prayer. Whoever omits it, whether deliberately or by forgetfulness, or replaces it with another remembrance (dhikr), his prayer is valid and he does not perform sujūd al-sahw. Shaykh al-Islām Imam al-Nawawī (may Allah have mercy on him) said: “Our school holds that one does not prostrate for omitting the audible or silent recitation, the tasbīḥ, and the rest of the hayʾāt.” [al-Majmūʿ, Vol.4/p.127]
If he performs sujūd al-sahw for something that does not call for it, his prayer is invalidated, because he introduced a prostration of forgetfulness without a cause, and he must repeat the prayer. The exception is one who did so out of forgetfulness or ignorance, whether because he recently entered Islam or because he lives far from scholars; he is excused and his prayer is not invalidated.
It is stated in Mughni al-Muḥtāj (Vol.1/p.417): “It is stated in al-Anwār: If he does something that does not call for sujūd al-sahw, thinking that it does, and then prostrates, his prayer is not invalidated if he is ignorant because he recently entered Islam or because he is far from scholars.”
Since this issue is hidden from the laity, as it is among the subtleties of knowledge, and the laity are excused for ignorance of whatever is of such a nature, and their act of obedience is not invalidated because of it, it may be said that the prayer of one who has not acquired knowledge of the issue is not invalidated. As for after knowing it, the prayer is invalidated.
Whoever realizes while still in the prayer that his prostration was out of place, it is sunnah for him to perform sujūd al-sahw. And Allah Almighty knows best.