"Nac ydy, dyw hi ddim yn gallu coginio."
Translation:No, she is not able to cook.
It would depend whether the meaning was not able to undertake the task now or not having the ability to do it ever.
'Gallu' can be the verb 'to be able' or the noun 'ability'
The English is ambiguous here and so I've added your suggestion as a possible correct answer.
If we wanted to say 'she is unable to cook' meaning she doesn't have the ability to cook (rather than she is unable to cook.....because of time,work etc)
We would say 'does dim gallu coginio gyda hi ' = she has no cooking ability.
This has ydy (nac ydy) together with yw (dyw hi ddim) -- would that be common?
I thought that people used either one or the other.
Yes, this is how it would be said in the south. In the north we use "Ydy" as fully interchangeable with "Yw". In the south "Yw" is for statements whereas "Ydy" is for questions, I think it's the same in Cornish. "Usi hi lowen?, "Usi, Lowen yw hi." (I think I'm correct here, but I'm from the north, so I'm not one hundred percent sure)