You should capitalize island when it is a part of a proper name. For example: Long Island, Gillian's Island.
No they shouldn't be capitalized.
Yes, season names are capitalized when writing.
Capitalize titles in writing and grammar when they come before a person's name, as in "President Lincoln." However, do not capitalize titles when they are used generically, like "the president announced a new policy."
If you are writing something with a title, you would capitalize Happy Holiday Season in the title. If you are writing it in something other than a title, you would not capitalize it.
Yes, you should capitalize the first letter of each word in "Thank You" when writing a thank you card as it is a proper noun.
In a formal writing, yes. In an informal writing, you don't have to.
Yes, always capitalize a state.
No they shouldn't be capitalized.
If you are writing in APA style (and I assume you are), you do not capitalize the names of theories or hypotheses.
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Yes, in writing, you should capitalize the names of books.
Yes, you should capitalize abbreviations when writing them in a formal document.
You only capitalize "village" if it is part of a proper name. e.g "That is White Village; it is a very nice village."
Yes, you should capitalize the word "Figure" when referring to a figure in a paper.
Yes.
Yes, acronyms are typically capitalized when writing.
Yes.