Finally, since I haven't tried using the opening explorer, can someone tell me the specific rules on the use of it, or provide a link? I cannot find a link on the subject at the moment.
https://support.chess.com/customer/portal/articles/1444857-how-do-i-use-the-game-explorer-
Ask yourselves the following questions: Does chess.com want you to learn? (Yes). Is using the openings explorer allowed in correspondence chess? (Yes). Is it meant to provide you with a resource to help you learn? (Yes). Are you allowed to use it throughout the entire game? (No).
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At the same time, I see one other view from the other side of this argument: If you sat down with someone at a coffee shop to play a game of chess, how would you feel if, after the first few moves, your opponent whips out a gigantic book to pinpoint what kind of opening you have in mind? I would be against that.
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The answers to your questions are 1. who cares? ,2. yes, 3. yes, 4. yes.
Actually, in a coffee shop I wouldn't care. If I were playing a tournament I would cite the appropriate article in the laws of chess to the TD.
More to the point, if you were playing in a coffee shop, assuming you were in the same coffee shop, you would not be playing correspondence chess. The rules for correspondence chess, much like chess itself are well established. Its worth knowing what those are.