Is it considered a degradation [of the prayer] if a worshiper recites Surat An-Nas in the first rak'ah and Surat Al-Ikhlas in the second rak'ah, knowing that he has not memorized any other surahs? And should he repeat Surat An-Nas in the second rak'ah or recite Surat Al-Ikhlas?

If a worshiper recites Surat An-Nas in the first rak'ah and then recites Surat Al-Ikhlas in the second rak'ah, there is no harm in it, and this is permissible. There has been disagreement regarding the dislike of reciting surahs in an order contrary to that of the Mus'haf (inverted recitation). However, the correct view is that there is no dislike in doing so, based on the actions of the Prophet, peace and blessings be upon him, and his Companions. A Muslim should be keen to learn and memorize the Qur'an due to the immense reward therein.