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 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.
I`m a mother of three orphans. Is it permissible for me to spend on myself from their salary, such as buying a Jilbab*?
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.
It is permissible to take a reasonable amount that is equal to your services to them. However, it is better that you don`t. The evidence on this is that Almighty Allah Says (What means): "Make trial of orphans until they reach the age of marriage; if then ye find sound judgment in them, release their property to them; but consume it not wastefully, nor in haste against their growing up. If the guardian is well-off, Let him claim no remuneration, but if he is poor, let him have for himself what is just and reasonable. When ye release their property to them, take witnesses in their presence: But all-sufficient is God in taking account." [An-Nisa`/6]. And Allah The Almighty Knows Best.
* A full-length outer garment, traditionally covering the head and hands, worn in public by some Muslim women.
What is the ruling on buying a car from someone for less than the market price, because they are in a hurry to travel and want to sell their belongings at a lower price due to their urgency?
Yes it is permissible; however, a Muslim shouldn't take advantage of other's difficult situations.