No it doesn't require to be capitalized.
no
It should be --- Earth Day, Planet Earth.
Since 'day' is a common noun, you should only capitalize it if at the start of the sentence or part of a name/title (Eg: Graduation Day 2013).
No, you should not. You should only capitalize a word when it is at the start of a sentence or when it is a proper noun.
It should not be capitalized.
yes, surey!
no
In the salutation "Good day to you," you only need to capitalize the first word, "Good."
The phrase "Columbus Day" is the full name of a holiday. Therefore, both words should be capitalized.
It should be --- Earth Day, Planet Earth.
The last day of the Christmas season (January 9th) is the Feast of Baptism of the lord. If you have a advent scripture book this should be the day that it ends.
Yes, you always capitalize a day of the week.
Yes, "Game Day" should be capitalized when referring to a specific event or occasion.
Yes, you should capitalize "About" in a title.
Yes, it should be capitalized because it is a proper noun
Hercules is not a saint and has no feast day.
Yes, "Day" should be capitalized in Mother's Day as it is a specific holiday and part of the proper noun.