I bought a character card from the coffee shop with the silver coins and don't know what happened to..

The character goes to your list of avatars. Tap on your profile picture, then the pencil next to your picture. Avatar characters give you no game benefit, and can only be seen by non-Facebook friends. It is more advantageous to buy energy upgrades for your drink (which benefit you and everyone who drinks it) or star box (which benefits you only).