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1. Add all the Adventure Deck 1 cards to your game box. Turn up the Adventure Path card "Rise of the Runelords", the Adventure card "Burnt Offerings", and the Scenario card "Attack on Sandpoint". Begin!
2. Officially, you should start that character over with no feats and all Basic cards. You should "re-run" them through all the previous Scenarios (the other characters can tag along, and while they can still pick up new boons, they can't get the rewards for Scenarios/Adventures they've already earned) so that they can keep up power-level-wise. Remember, a character only gets an Adventure Reward if they've completed all the Scenarios of that Adventure.
If you don't mind a character not getting certain rewards, you can just have the new character move forward with the survivors rather than replaying everything.
If a character dies, and the next Scenario is in Adventure 3 or higher, their replacement character can build their new decks out of any cards that are two AD numbers lower than the new Scenario.
3. You don't receive the reward for the Scenario, and if you want to earn the Adventure Reward, you'll need to attempt the Scenario again (and again) until you succeed. You can still use all the boons you acquired in play to rebuild your character decks.
4. See above about characters dying. Essentially, if a character dies, you're just adding all their cards back to the box and adding a new character (who may or may not have the same character cards). You can either start over, with the experienced characters cruising along to help keep the "newbie" alive, or just cope with the new character having fewer feats and crappier cards.
That said, it's your game. If you want to create advanced characters or what have you, ignore the rules and do whatever makes it fun.