Is my cousin's refusal to undergo surgery to remove the damaged part of her colon, and her reliance instead on treatment with the Quran, considered suicide, and is she sinful for this decision?

Leaving a sick person to undergo surgery is not considered suicide, as refraining from medical treatment is not deemed suicide by the majority of jurists. And whoever abstains from treatment until death is not considered disobedient, because healing is not necessarily guaranteed.