Is a wife considered divorced if her husband refused to go to bed with her(for sexual intercourse) for two months?

A wife doesn`t get divorced no matter for how long her husband refuses to have sex with her, and she had better go to court.

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..

Is it permissible for the doctor to uncover the hair of a female patient out of necessity?

It is only permissible for him to do so when there is no female doctor, and he should examine the patient in the presence of one of her Mahrams(unmarriageable kin).

Is Zakah (obligatory charity) due on articles of merchandise even if they were stacked in the merchant`s stores for years?

Yes, Zakah is due on stored articles of merchandise even if they were stacked in the merchant`s stores for years because this is the way Islam has countered monopoly.