I think ydw is like 'Yes, I am' and cei is like 'Yes, you may'.
gofyn is the normal form, but after the phrase "Ga i" the word "gofyn" gets a soft mutation and becomes "ofyn". you can read about soft mutations in the grammar section of this lesson. ^_^
Thank you! I forgot the 'g' often vanished in the soft mutation.
It's not really like "I do," it just simply means "yes," in response to that kind of question - it just sounds like "I do".