I think they did it that way because "baner" is feminine, and they don't want to confuse you with the mutation.

I think you did use the exact wording... pa/which liw/colour ydy'r/is the baner/flag cymru/of wales

Do you need the 'r there?

I would have thought that baner Cymru would be definite by default, since Cymru (a proper noun) is definite.

That would make sense but it is an incorrect translation of the sentence given.