1. The winning lottery numbers are three, fifteen, nineteen, and twenty seven.
Add a hyphen between "twenty and "seven".
You should always hyphenate numbers when you are describing compound numbers between twenty-one and ninety-nine.
2. At least one-fourth of the paintings—which are all by American artists—will be included in the special exhibit.
Delete the hyphen in one-fourth.
Fractions should always be hyphenated when they function as adverbs or ajectives. In this case, the fraction functions as a noun, so the hyphen is not needed (although there is differing opinions on this, so no revision is needed could also be correct).
Dashes are used to separate groups of words. It's longer than a hyphen and is used to indicate a range or pause. Hyphens are used to separate parts of words.
3. Mr. Singh, an accomplished musician, plays three instruments: piano, trumpet and clarinet.
Add a comma after "trumpet"
It is most accepted to include a comma after all items in a list. It is correct to set apart the rest of the sentence from the list with a colon.