Is it permissible to pay the Zakah (obligatory charity) for settling the debt of a deceased relative?
                                It is impermissible to pay the Zakah for settling the debt of the deceased since Zakah is paid to eligible recipients who are alive. As for the debts of the deceased, they are to be settled from the estate before dividing it amongst the heirs, but if the deceased didn`t leave an estate, then it is desirable for his/her heirs to settle those debts if they can afford them. And Allah Knows Best.
                             
                        
                            
                                
                                Is it permissible to make up for missed fast after the beginning of the second half of the month of Sha`ban (the month before Ramadan)?
                                Yes, it is permissible, but one who had missed fasts should hasten to make up for them. As for the Hadith mentioned in this regard, the prohibition is for offering absolute voluntary fasting. And Allah Knows Best.
                             
                        
                            
                                
                                What`s the ruling on using the following materials in manufacturing cosmetics: olive oil, Vaseline, talc powder, glycerin, honey, almond oil, pine oil, galingale and marjoram?
                                All perfect praise be to Allah, The Lord of The Worlds, and may His peace and blessings be upon our Prophet Mohammad and upon all his family and companions.                                                                                                                                                                                                                                    None of the above materials is forbidden, and it`s lawful to use them in manufacturing products that are beneficial to people. This is because, in principle, all things are lawful so long as there is no evidence in Sharia indicating otherwise. And Allah Knows Best.
                             
                        
                            
                                
                                I have mixed (halal and haram) money, and I want to purify it. My father is poor, and I want him, my mother, and my mother-in-law to perform Hajj, along with myself and my wife, as they need care due to their old age. Is it permissible to use this money for Hajj, or what should I do with it? Please advise.
 
 
 
 
 
                                If you knew the exact amount of unlawful money, then you should give as a charity, and if didn't then try to figure out the closest amount in order to give it as a charity. 
As for performing Hajj, perform it by using your lawful money. May Allah Bless you for being dutiful to your parents and your mother in law and for your attempt to serve them, And Allah Knows Best.