Is the questioner's mother sinful for what happened to her grandfather, and what should she do, and what is your advice to her if she is not sinful?

Your mother bears no sin for your grandfather's fall and death, so long as she left him to clean himself. His actions after her departure, his getting up, and his fall are not her fault. It is recommended to pray for mercy upon him, frequently seek forgiveness for him, give charity on his behalf, and perform Hajj and Umrah (definition) for him.