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 the Aqeeqa due on the newborn in case of dying almost a month after the delivery?
                                Offering Aqeeqa after a week of a newborn death is recommended.
                             
                        
                            
                                
                                Is it a condition that the meat of the Eid sacrifice should be distributed in order for the sacrifice to be accepted by Allah?
                                The poor and needy should be given from that sacrifice , even if it be a small portion,(One kilo for example) as raw meat so that they would cook it the way they want. The remainder of that sacrifice is either distributed, eaten, or offered to people in a banquette .
                             
                        
                            
                                
                                Is Zakah (obligatory charity) due on the items used in the trading process such as: cars , shops etc..?
                                No Zakah is due on equipments used in the trading process such as cars and the like.