Is it permissible for a woman to ride a taxi without a Mahram (unmarriageable kin) in order to attend a gathering of knowledge?
It is permissible for the woman to pursue the knowledge that she needs in order to perform the religious requirements due on her if there was nobody to teach her at home, provided that there is no temptation involved. Moreover, we don`t recommend that she rides a taxi without a Mahram although such an act isn`t from the forbidden Khulwah (seclusion).
Does using a wet miswak while fasting break the fast?
A fasting person should ensure that the miswak is dry when using it.
However, if the miswak is slightly moist but does not release any liquid when squeezed, then its use does not break the fast.
What is the ruling on istinja' after urination, and is it done with water and soap or with water only?
Istinja' from urine and stool is obligatory. It is permissible to perform istinja' with water alone, or with toilet paper alone. The best way is with toilet paper then water. If one wishes to suffice with one of them, then water is better. And Allah the Almighty knows best.
Is it permissible to eat from an Udhiyah slaughtered on behalf of a deceased person?
Praise be to Allah, and prayers and peace be upon our Master the Messenger of Allah.
It is permissible to eat from the sacrifice (uḍḥiyyah) that is offered on behalf of a deceased person. This is the madhhab (school of thought) of the Hanbalis. In this case, the heirs take the place of the deceased as if he were alive, with the same rights to eat from it, give it in charity, and offer it as a gift.
It is stated in Maṭālib Uli al-Nuhā (Vol.2/P.472): "Offering a sacrifice on behalf of a deceased person is better than offering one on behalf of a living person, because the deceased is unable (to perform deeds) and is in need of reward. It is to be treated like a sacrifice on behalf of a living person in terms of eating, giving charity, and giving gifts." And Allah Almighty knows best.