Yes, Labor Day is the name of a specific day, which makes it a proper noun, so it is capitalized.
If it's part of a persons title, then it needs to be capitalized. If you write "I want to be a labor and delivery nurse", then it doesn't need to be capitalized.
Yes. Day is capitalized in Mother's Day and Mother's has an apostrophe before the "s."
The phrase "Martin Luther King Day" is correctly capitalized. Martin Luther King is a name so is automatically capitalized. Since it is a specific day, a holiday to be exact, day is also capitalized.
Materials, labor and overhead.
I would think a day or two before Labor Day ... Is there no end to my IQ
No, because it is n ot a proper nou n.
Yes it is. "Mother's Day"
Yes.
Yes, "Graduation Day" should be capitalized because it is a proper noun referring to a specific event.
Yes, in the phrase "Election Day," the word "Day" should be capitalized because it is a proper noun referring to a specific day on the calendar.
Labor Day