What amount of blood discharged from a human body is considered among the things that invalidate fasting, and does half a cup of blood discharged due to swollen veins in the anus invalidate the fast?

Your fast is valid, and you are not required to do anything as long as the blood exits due to illness and without your action. The blood that invalidates the fast is that which exits due to a person's action and choice, such as cupping (hijama) or phlebotomy if it is abundant and affects the body. As for blood that exits unintentionally, such as from an accident, nosebleed, or wound, it does not invalidate the fast, even if abundant, unless it weakens the person, in which case they are permitted to break their fast and make it up later.