Is it permissible for a person who had vowed to give a certain amount of money to another, but didn`t find the latter to donate that money to the mosque?

In principle, the vowing person should abide by his vow as much as possible. Therefore, if he couldn`t find the person that he had made the vow for, then the vow itself is countless and nothing is due on its maker. However, if the latter happens to find the former later on then, he has to give him that money.

 Is it permissible to pay the Zakah to my grandmother who lives alone in a rented accommodation with bad conditions noting she had three sons. 

Zakah cannot be given to ascendants (parents and grandparents). It is obligatory for her sons and grandsons to provide for her, and they would be sinful if they fail to do so. And Allah Knows Best.

 By slip of the tongue, my son cursed Allah. It is worth pointing that he has concluded his marriage contract recently, but haven`t consummated the marriage. What is the position of Sharia on this? 

What is the ruling on the financial leasing transaction in commercial bank?

Any transation that is involved in the unlawful is impermissible. And Allah Knows Best.