Is it true that if a ritually impure, or a menstruating woman visits one who is in confinement, harm will be inflicted on the latter, or her baby?

This is completely wrong and unfounded piece of information.

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..

A woman didn't fufill fasting of the month of Ramadan two years ago, due to pregnancy and breastfeeding, at the time being she is making up the missed Ramadan. What is the ruling of Sharia? And what is due on her? 

Is it permissible for me to name my daughter "Leen"?

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