Dear E:

You wrote:

James, in formal writing and when writing business documents; is it proper to use contractions, such as it’s for it is, or not?

In formal writing avoid contractions when possible.

Also, should I put quotation marks around game titles, game modes, and business document titles? Or, only the titles of books, stories, poems, and the like?

Not documents. Games are like works of art, so normally they are italicized or underlined. Quotation marks are for titles of parts of works (like chapter titles) or shorter works (short stories, poems, songs).

Which type of dash should I use after the word date in the sentence below? And is it proper to use dashes in business documents?
I do study English Plus grammar lessons, but there’s some which don’t make sense to me at first–all the questions I ask you.

Use the standard em dash, I guess. Dashes are fine as long as they are not overused. Dashes are for emphasis like exclamation points, so they can be overused.