The battle talents-pips, boosts, defense, cards, etc-that your storm hound may develop will depend on what is achieved when your pet becomes ancient and epic, which is when new talents will be revealed. If you have a card already then you probably won't get any others. For a fuller explanation of Advanced Pets check out link below for details from the Advanced Pets update.
Greetings and welcome. Your pet will only give you cards for what it says (in this case as a baby). Your pet will very very rarely ever cast spells in duels (ultra rare ability). Otherwise, it depends on the abilities it develops while you are leveling it. It will have two different sets, duel and derby abilities. Hope this helps!
If you have a pet that comes with a card, it could come with another card, but it is very rare. Trained all of my giftcard pets and one came with a blade for minion card.