Is it obligatory to have an intention (niyyah) for every prayer?
Praise be to Allah, and peace and blessings be upon our Master, the Messenger of Allah.
It is obligatory for the worshiper to have a specific intention (Niyyah) for every prayer, meaning they must consciously intend the act of worship they are performing. The intention is a pillar (Rukn) of the prayer, and the prayer is not valid without it. It is not a requirement to utter the intention verbally; rather, doing so is considered a recommended Sunnah. And Allah the Exalted knows best.
Is it incumbent on a father to cover the marriage costs of his son if the latter couldn`t afford them?
The son should seek the help of his relatives in order to convince his father to do the aforesaid, and the father should make sure that his son doesn`t commit fornication through helping him to get married, and Allah will reward him for doing so.
Should a prayer performer who forgets to offer the middle Tashahod (saying ash-hadu anala ilaha ila-alah) offer Sujood As-Sahw (prostration of forgetfulness)?
He/she should offer two prostrations of forgetfulness at the end of the prayer. And Allah 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.