QUES: The plane leaves without letting me have

correct the punctuation.

CORRECTED: The plane leaves without letting me have.

QUES: Eat healthy and enjoy nature in their spare time represents one of the pedestals of Korean culture

correct the punctuation.

CORRECTED: Eat healthy and enjoy nature in their spare time represents one of the pedestals of Korean culture.

QUES: Where no age limit is specified the general age limit of 6 years old applies

correct the punctuation.

CORRECTED:
Where no age limit is specified, the general age limit of 6 years old applies.