I think the first one is a sweet that appears in the lyrics of the famous song from Calamity Jane, 'The Deadwood Stage'. If you Google the lyrics you should see something 'good enough to eat'.
I associate Calamity Jane with a rifle and with a T in front is certainly a dessert associated with Christmas. ("C wouldn't be C without a booze-laden t". I loathe them!) However, I can't parse that.
I would have thought that a play - at the theatre - which is a 'calamity' would make 'turkey' the better answer.
And there are plenty of Cornish villages called St. xxx but not too many with only 5 letters. That said, I can't find one that fits the clue!