What does "mae" mean here ?
mae Owen... - 'Owen is...'
What is the relevence of 'yn' please?
yn/'n is used here to link the verb Mae... ('is', as in 'Owen is...') with verb-noun bwyta (eating). It is not translated into English in this usage.
This is outlined in the notes for the section 'Present1' earlier in the course.
Also see this.