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..
What is the ruling on memorizing the Quran during menstruation, knowing that I do not read directly from the Quran but from a paper or from my phone?
It is not permissible to memorize the Quran during menstruation because memorization requires repetition, and a menstruating woman cannot touch the physical pages of the Quran. Similarly, if the Quranic verses appear on the screen of the phone, it is considered like touching the Quran. And Allah Knows Best.
What is permissible for the husband to do as far as having sex with his wife is concerned?
The couple are free to enjoy each other sexually provided that they don`t do it during menses. It is also forbidden for the husband to enjoy the wife from her anus.
What should a sick person, who is incapable of fasting, and who didn`t make up for missed fasting days, do?
One who has missed fasting days is obliged to make up for them, but if he/she wasn`t able to because of an incurable disease , or old age, then he/she has to pay a ransom which is feeding a needy person for each of the missed fasting days. And Allah Knows Best.