To add a card is to place a card in the hand.
Drawing a card is considered to be a specific method of adding a card from the Deck to the hand, so effects that deal with drawing will not deal with all adding. For example, "Protector of the Sanctuary" will not prevent adding with an effect like "Archfiend's Oath". However, effects that deal with adding will also deal with drawing, so if "Blackwing - Breeze the Zephyr" is drawn by a card effect, then you can use its effect to Special Summon it.
You do not lose the Duel if you have no cards in your Deck when required to add a card from it, only when specifically drawing.