All the prophets and their divine successors are infallible and sinless as they are the best examples to be followed by human beings. Allah (SWT) ordered all human beings to obey the prophets and their successors. If God forbid, they do any sinful act, it means that Allah (SWT) is ordering us to commit sin following them, which is impossible.
Sura al-Nasr like many other Surah have been mistranslated. It does mean at all to seek forgiveness for the prophet himself but for the Muslims who enter in the Religion of Allah for their past sins.
Every verse in Quran and every Hadeeth on this matter means that the Prophet is seeking forgiveness for the Believers.