What is the ruling on performing dry ablution (tayammum) instead of the ritual bath due to severe cold?
Whoever is sick such that he cannot use water, or finds the water cold and heating it is not possible, and the person would be harmed by using cold water, it is permissible for him to perform tayammum. He must make up what he prayed with tayammum, because this is a place where there is water. And Allah the Almighty knows best.
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.
A person who has recently embraced Islam is afraid of undergoing circumcision (khitān) — what should he do?
All praise is due to Allah, and peace and blessings be upon our master, the Messenger of Allah ﷺ.
If this person would be harmed by undergoing circumcision, based on the assessment of a trustworthy physician, then he is not obligated to undergo it. However, if the matter is simply a fear of the procedure itself, then it may be postponed until he feels at ease and settled about it, provided this does not lead him to become averse to Islam — while still taking care to remove any impurity from the concealed area [beneath the foreskin]. And Allah, the Exalted, knows best.
What is the ruling on forgoing the sacrifice (uḍḥiyah) for one who is financially able to offer it?
Praise be to Allah, and peace and blessings upon our master, the Messenger of Allah.
It is disliked (makrūh) for one for whom the uḍḥiyah (sacrifice) is recommended (Sunnah) to forgo offering it, on account of the scholarly disagreement regarding whether it is obligatory. And Allah, the Most High, knows best.