*Ydw. As you'll learn at some point in the course "yes" and "no" changes depending on the question being asked. Here you need "ydw" as the answer is "Yes I do".
Can you give an example of a question for which the answer would be "oes"? (For example, would the question "Can you sing?" be answered "Oes"?). Diolch.
[Would that be "Allwch chi ganu?" ? ]
Oes gen ti gar? Oes. "Do you have a car? Yes I do."
Oes llyfr gyda ti? Oes. "Do you have a book? Yes I do."
Oes ci yn y tŷ? Oes. "Is there a dog in the house? Yes there is."
If you ask with oes, the "yes" answer will be oes.
The answer to Allwch chi ganu? would be Gallaf. -- again repeating the verb. Oes? Oes. Allwch? Gallaf. Dych? Ydw. (Is there? There is. Can you? I can. Are you? I am.)
If you want to answer no to "do you like Welsh?" The answer would be nac ydw. To a question where the positive answer is oes, the negative would be nac oes.