Level select:
Hold A + B at the options screen.

Invincibility in level 1:
While playing level 1 (The Pridelands), intentionally allow any lizard or porcupine to hit you three times. You have one more hit left. Then press Down to duck completely and let any animal hit you two more times. A life counter will appear, but it will never get lower than zero. This can be done in any stage except the second one.