ireland in Welsh is Yr Iwerddon it needs the definite article
The old name for Ireland in Welsh was 'Y Werddon' which is the equivalent of 'The Emerald Isle' from Gwerddon = A green place or glade.
Modern spellings have evolved to 'Iwerddon'
No, it doesn't, at least I've never seen it with the definite article. Maybe you're thinking of "Scotland" which is "Yr Alban".
No it doesn't.