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 (peace and blessings be upon him) 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 (peace and blessings be upon him) 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.”{Related by Bukhari & Muslim}.
However, not all the deceased are in the same situation because Allah the Almighty says, "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 man to go out wearing shorts?
It is permissible as long as his Awrah(private part), which is between his navel and knee, is covered. However, the regular wear traditions and modesty are to be observed.
Is it permissible for me to name my newborn baby boy “Al-Moustafa” ?
There is no harm in naming your son “Moustafa” without using the ”Al”.
What should a woman who is in a state of menstruation, or confinement do if she became ritually pure during the day of Ramadhaan ?
If she became pure during the day time of Ramadhaan, it is desirable for her to fast the rest of that day, and to make up for it along with the days that she had missed due to menstruation.