Is it permissible for a person to give the Zakah (obligatory charity) to his daughter-in-law?
Yes, it is permissible for a person to give the Zakah to his daughter-in-law if she was poor, and none provided for particularly by whom are obliged to provide for her. And Allah Knows Best.
What are the conditions for the validity of the slaughtering process according to Sharia?
Praise be to Allah, and peace and blessings be upon our master, the Messenger of Allah.
Regarding the Sharia-mandated conditions for the validity of the slaughtering process (Adh-Dhabh), they are as follows:
The Identity of the Slaughterer: The person performing the slaughter must be either a Muslim or from the People of the Book (Christian or Jewish).
The Required Cuts: Both the trachea (windpipe/breathing passage) and the esophagus (food passage) must be completely severed.
Stability of Life: The animal must possess stable life at the start of the slaughtering process. This is identified by clear signs, such as vigorous movement or the forceful gushing of blood after the throat and esophagus are cut.
The Tool of Slaughter: The tool used must be sharp, capable of cutting or piercing by its edge and not by its sheer weight or blunt force.
And Allah the Almighty 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.
Is it permissible for the person who hasn`t made wudu` (state of minor ritual impurity) to perform the Adhan?
Praise be to Allah, and peace and blessings be upon our Master, the Messenger of Allah.
It is disliked (Makruh) for a person in a state of minor ritual impurity (Hadath Asghar) to perform the Adhan. However, if he does so, his Adhan is considered valid and fulfills the sunnah of the Adhan despite it being disliked. And Allah the Exalted knows best.