Is it permissible for the wife to give the Zakah (obligatory charity) of her money to her poor husband?

Yes, it is permissible for the wife to give from the Zakah of her money to her poor husband. And Allah Knows Best.

Does the deceased hear the supplications or recitations of those visiting his/her grave? And does making constant supplications for the deceased who didn`t adhere to performing the prescribed prayers ameliorate his/her affliction?

Praise be to Allah the Lord of the Worlds.

In principle, the dead hear the living since it has been rigorously authenticated that the Prophet (PBUH) ordered the bodies of the idolaters slain in the Battle of Badr to be buried. He then approached them and called them one by one and said: "Have you found what your Lord promised to be true for we have found what our Lord promised us to be true." Umar asked him: "O messenger of God! Why do you speak to lifeless bodies?" The Prophet (PBUH) replied: "By the One Who has sent me with the truth! You do not hear my words better than they do except that they cannot respond." [Agreed upon].

However, not all the deceased are in the same situation because Allah The Almighty Knows: "Before them is a Partition till the Day they are raised up." [Al-Mu`minun/100]. Moreover, supplication reaches the deceased. And Allah Knows Best..

After buying tires, I made an oath not to buy tires from a person. Afterwards, he offered his entire car for sale. What is the ruling on this?

If you bought the entire car and in order to be on the safe side, you should pay an expiation; feeding 10 poor people and the cost of feeding a person is half a JD. And Allah Knows Best.

Is a woman`s face an Awrah (a private part) that should be covered?

During prayer, a woman`s whole body is a private part except the hands and the face. Outside the time of prayer, scholars are of the view that a woman should wear on her Islamic attire to avoid temptation.