is the sentence “My parents visited Europe in January, 2013.” correctly punctuated

Yes, the sentence “My parents visited Europe in January, 2013.” is correctly punctuated.

is the sentence “ The Stand, remains Stephen King’s best-selling work.” correctly punctuated

Yes, the sentence "The Stand remains Stephen King's best-selling work." is correctly punctuated.

is the sentence “ The Stand, remains Stephen King’s best-selling work.” Incorrectly punctuated

Yes, the sentence “The Stand, remains Stephen King’s best-selling work.” is incorrectly punctuated. The comma is not needed because "The Stand" is not an introductory phrase or clause. The correct punctuation would be: "The Stand remains Stephen King's best-selling work."

is the sentence “Our sun is a start; the stars we see in the night sky are actually far-away suns.” correctly punctuated

No, the sentence “Our sun is a start; the stars we see in the night sky are actually far-away suns.” is incorrectly punctuated. There should be a spelling correction (star instead of start), and a punctuation correction.

Corrected sentence: "Our sun is a star; the stars we see in the night sky are actually faraway suns."

is the sentence “Our sun is a star; the stars we see in the night sky are actually far-away suns.” correctly punctuated

Yes, the sentence “Our sun is a star; the stars we see in the night sky are actually far-away suns.” is correctly punctuated.

is the sentence “Our sun is a star, the stars we see in the night sky are actually far-away suns.” correctly punctuated