What is the ruling of Islamic law regarding money deposited by a grandmother into her grandson's account without his knowledge before her death? Is she sinful for that? And what is the ruling of Islamic law regarding a grandmother selling half of her properties to her grandson before her death?

There is no sin on the grandmother for not being equitable among her children and grandchildren in a gift. If her grandson knew about the amount the grandmother placed in his account and accepted it before her death, then it is a valid gift. However, if he did not know about it or accepted it after her death, it reverts to the estate. Similarly, what was written for him regarding half of her properties after her death reverts to the estate, because a gift is not valid if the giver dies before the donee knows about it and accepts it. A gift is only valid if it is taken possession of during the giver's lifetime.