What is the ruling on a son paying off his father's debt with his own money without his father's permission? Is this considered theft? Is he required to return the amount after paying it off? And is it permissible for him to eat and buy from the grocery store in this situation?

It is not permissible for a child to dispose of his father's money without his permission, unless the father withholds the obligatory sustenance from his needy child. In that case, it is permissible for the son to take his sustenance in a reasonable manner. Therefore, your disposing of your father's money and paying off his debt without his permission is an error, and you are liable for the money you took, unless the father permits it. You should inform your father of what you did and apologize to him, or return the money without informing him if you fear harm. You are not responsible for paying off his debt, and you are permitted to eat from his money despite him being a procrastinator, because his money is lawful.