To get to the Save Menu without dieing, go into the subscreen by pressing start and press Up and the Select button simultaneously. The options will be Continue, Save, and Retry. If you use this on the overworld, continue starts you at the area you begin the game at. In the underworld, it puts you at the start of the labyrinth you were in. Save obviously saves your game and puts you at the Save Game Select menu. Retry takes you to the Save Game Select menu and doesn't save your game.

To start a game at the second quest (after you've beaten it once), enter your name as "ZELDA".