After one of those two things has happened, you can choose to draw two and then choose two cards from your hand to discard
If you are capable of healing your cards, through items, actions, or character abilities, and Beast, Tragic Hero has damage on them at the start of your turn, you can let them attack and then heal them, allowing you to still benefit from the increased strength but keeping them healthy enough to stick around
Once a card moves on from the graveyard or the battlefield straight to exile, you get to draw a card and lose a life, which is a fair trade-off
When a character quests, it immediately earns you a certain amount of Lore points, indicated on the card (look for a number of lore symbols on the card)