Since when did V/Ns mutate after yn?
You don't say, "dw i'n fwyta", rather "dw i'n bwyta", so surely it would be "meddwl", here?
It's not mutating after yn, it's mutating after an invisible ei which is usually not spoken any more (but occasionally written).
The Tips and Notes for this lesson now explain this: https://www.duolingo.com/skill/cy/Opinions (section "What do you think of...").
Why is it "wyt"? In the notes "rwyt" is used ("Beth rwyt ti'n feddwl o'r etholiad?").
Where's the mutation on "Ceri" ?
People's names usually don't mutate.
"Wyt" is more often used in spoken Welsh, although it is written here in the south too. At least that is my understanding.