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 to listen to chants praising the Prophet if accompanied by musical instruments?

If singing, or chanting in praise of the Prophet was accompanied by a forbidden musical instrument, then it is forbidden.

How long is the` Iddah(waiting period) of a divorced woman?

If a woman is pregnant at the time of divorce, then her 'Iddah (waiting period) expires when she gives birth to the baby. If she is in a state of menstruation, then her `Iddah expires when she finishes three menses. However, if she doesn`t have menses, then her `Iddah expires after three months.

Is it permissible for the guardian to give Sadaqa( voluntary charity )from the money of the orphans?

It is impermissible for the guardian to donate from the money of the orphans because he is entrusted with the safekeeping of that money, and is prohibited from donating it.