Should a worshiper say "Alhamdulillah" if he sneezes during prayer, and should he say "A'udhu billahi minash-shaytanir-rajeem" if he hears the braying of a donkey while praying?

It is permissible for the worshiper to praise Allah if he sneezes during prayer, due to the السنة (Prophetic tradition) mentioning this and the Prophet (peace be upon him) not disapproving of those who did so.

As for seeking refuge (A'udhu billah) upon hearing the braying of a donkey during prayer, it is preferable not to seek refuge, because it relates to something outside of the prayer, and the worshiper should not occupy himself with matters external to it. There is no difference in this regard between obligatory (Fard) and supererogatory (Nafl) prayers.