Is it permissible for the man to go out wearing shorts?
All Perfect Praise is due to Allah, The Lord of The Worlds
It is permissible so 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. 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..
Should nail polish be removed before making ablution?
Yes, it should be removed because it prevents water from reaching the nails.
Is it permissible for a teacher to have one of the school meals originally allocated to students considering that there is plenty of them and they may spoil?
All perfect praise be to Allah the Lord of the Worlds. May His peace and blessings be upon our Prophet Mohammad and upon all his family and companions.
The Ministry of Education has the final say in this regard because it isn`t allowed to take from public funds save with the permission of the body in charge of spending from it. In fact, we have sent a letter to the Ministry concerning this issue and we are waiting for an answer. However, to prevent spoilage of the meals, they can be sold and the price kept in favor of the students or distributed amongst the students themselves. And Allah The Almighty Knows Best.