Free discussion and deception are fundamental parts of the game.
You may say anything you want at any point during the game, including giving away information, lying, misrepresenting, or challenging other players. When you hold secret information, such as your character or loyalty, you may tell the truth about that information, mislead or lie, or refuse to discuss it.
However, you may not actually reveal your character or loyalty card at any point (since that would remove the possibility of tricking other players, which is fundamental to the game). In the same way, you may not try to "prove" you have a particular character card by describing the art on the card or other physical features. (Exception: some special characters allow you to look at another player's loyalty card.)