Why is it sometimes "Plaid Lafur" and sometimes "Y Blaid Lafur"? For example, when the sentence was "The Labor Party won a lot of seats," it marked "Enillodd y Blaid Lafur lawer o seddi" as wrong for using "y."
Because "Yn" when it means "in" causes a nasal mutation, and "C" when it nasally mutates to "Ngh" and "yn" itself becomes "yng".
This is explained earlier in the course in the notes for the section on 'Countries'.
Like Dave Carver, I would like to know what "the Welsh Labour Party" would be as this is what I normally hear in English.
For 'The Welsh Labour Party' it would still be 'Y Blaid Lafur yng Nghymru'.
However, a phrase more often heard to refer to that party in the news and in the Assembly is 'Welsh Labour' - 'Llafur Cymru', or occasionally 'Plaid Lafur Cymru'