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.

What is the ruling on having slight discharges of menstrual blood during a day of Ramadhaan, and before Maghrib time ?

A woman who is certain that her menses have started during a day time of Ramadhaan is in a state of menstruation, and her fasting is considered broken at first sight of blood. However, she is rewarded for not breaking fast at the beginning of day time.

Is the Saum(Fasting) of someone who ate and drank forgetfully while offering fasting of oath expiation invalidated ?

Whosoever eats, or drinks forgetfully is exempted by Allah; therefore, he/she shouldn`t break their fast whether it was obligatory, non-obligatory, or expiatory.

Is it permissible for me to name my daughter “Leen”?

“Leen” means “ease”, and there is no harm in giving your daughter that name.