What is the ruling on using toothpaste during the day in Ramadan?
Using toothpaste does not break the fast as long as nothing reaches the body cavity. However, it is disliked (makruh).
It is preferable for a fasting person to use it before the time of fast starts or after Iftar (breaking the fast) to avoid risking their fast.
If a father stops his daughter from getting married, is it permissible for her to conclude the marriage contract herself?
It is permissible for the father to stop his daughter from getting married if there was a lawful reason for that, and she isn`t allowed to conclude the marriage contract without her guardian. However, if her father denied her right in getting married for an unlawful reason, then she should go to court.
Does buying meat equivalent to the weight of a slaughtered animal and distributing it avail for an udhiyah?
Praise be to Allah, and prayers and peace be upon our Master the Messenger of Allah.
That does not avail for the sacrifice (uḍḥiyyah), because the sacrifice necessarily requires slaughtering an animal from the category of anʿām (camels, cattle, and sheep/goats) within a specified time.
Rather, that is considered a form of charity (ṣadaqah) for which one is rewarded. And Allah Almighty knows best.
What is the ruling on the ablution of one who washes his arms from the wrist to the elbows?
In the school of Imam al-Shafi'i (may Allah have mercy on him), washing the arms (hands) is achieved by washing the arms completely, from the fingertips to the elbows. Washing only the palms at the beginning is insufficient, as washing them at the beginning is a Sunnah, but after washing the face, it becomes obligatory (fard). The person performing ablution must wash his palms along with the arms after washing the face. If he does not wash his palms, his ablution is invalid and not correct. And Allah the Almighty knows best.