Is it permissible to say: "O Allah, by the status of the saints and the righteous, and our master Muhammad, peace be upon him, grant us the ability to reach Ramadan"?
                                What is mentiond by the righteous predecessors that they used to say: "O Allah bless us in Shaba'an and Rajab and give us the ability to reach Ramadan." [Shoa'ab Al-Iman/vol.3/pp.375]. 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.
                             
                        
                            
                                
                                If a father stops his daughter from getting married, is it permissible for her to conclude the marriage contract herself?
                                It is permissible for the father to stop his daughter from getting married if there was a lawful reason for that, and she isn`t allowed to conclude the marriage contract without her guardian. However, if her father denied her right in getting married for an unlawful reason, then she should go to court.
                             
                        
                            
                                
                                What is the ruling of Sharia on woman shaking hands with non-Mahram man?
                                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.
The Messenger of Allah (PBUH) said: "It is better to be stabbed in the head than touch a woman to whom one isn`t related." [Transmitted by Al-Tabarani /Al-Mo`jam Al-Kabir, Hadith No.16880]. Accordingly, it is forbidden for men to shake hands with non-Mahram* woman. And Allah The Almighty Knows Best.
 
 
* The women/men that you are allowed to marry. It includes all women/men other than mahram (including cousins).