While this is true in the general case, The Coin is an extra card added to your hand at the beginning of the game and is never a part of your deck. It is purely beneficial.
It is. Additionally the person who gets the Coin also gets an extra card in their starting hand. You can "mulligan" this card, or swap it out of your starting hand for another draw. Although this might seem relatively trivial, having an extra chance to mulligan a card increases your chances significantly of getting a card that you want in a specific matchup.