Is the worshipper sinful, and is his act considered valid if he repeated the Asr prayer after its time had expired, knowing that he doubted the last Tashahhud and did not perform the prostration of forgetfulness (sujud al-sahw) in the first prayer? And is his first prayer sufficient?

Whoever repeats the final Tashahhud out of forgetfulness or doubt about having performed it, then repeats it, is not required to perform the prostration of forgetfulness (sujud al-sahw). Re-performing the prayer in this case is incorrect, but there is no sin in it, and the first prayer is valid.