Do good deeds absolutely expiate evil deeds, even major sins, based on the verse {Indeed, good deeds do away with evil deeds} and the narration of the prostitute, or is this statement without merit?

Good deeds and the performance of obligatory acts do not expiate major sins. Rather, major sins require repentance. This is the view of Ahl al-Sunnah and the consensus of the Ummah, based on the Almighty's saying: "And turn to Allah in repentance, all of you, O believers." Thus, repentance is an obligation, and major sins are not effaced except through repentance, or through Allah's mercy and grace. As for minor sins, they are expiated by good deeds.