1. Veteran’s Day Veterans’ Day Veterans Day
-Which is grammatically correct? Why? -What sources could you use to find be sure?
Veteran’s Day
Veterans’ Day
Veterans Day

6. No Apostrophe Makes “Veterans” an Adjective
If you don’t put an apostrophe at the end of “Veterans,” you’re using the word as an adjective that modifies “Day.”
Just as “tree” tells you what kind of farm I’m talking about in the phrase “tree farm,” and “golf” tells you what kind of club I’m talking about in the phrase “golf club,” “Veterans” tells you what kind of day I’m talking about in the phrase “Veterans Day.”

7. Mother’s Day AND Father’s Day: CORRECT WITH APOSTROPHE
The original campaigner for creating Mother's day, Anna Jarvis, explicitly wanted an apostrophe, and she wanted it to be before the “s”
it was to be a singular possessive, for each family to honor their mother, not a plural possessive commemorating all mothers in the world

8. “April Fools’ Day” or “April Fool’s Day”?
Depending on the dictionary you use…
The Oxford English Dictionary shows April Fool’s Day. 
The American Heritage Dictionary lists April Fools’ Day.
And Merriam-Webster’s Dictionary lists April Fools’ Day with April Fool’s being a variant of the name.