How to unlock new maps/chapters?

When you clear all stages of a world, you will automatically move to the next world. You can also re-play previous worlds by tapping on the current world icon and swiping backward (or forward if you want to select the superior worlds)

How to level up my hero? 

Your hero will start at Level 1 each time you start a new game, and to level up, kill as many monsters as possible.