Only when you complete the Easy mode to access Normal, then the Normal mode to access Hard.
Your health will be restored as you successfully hit targets and avoid taking more damage so try and hit more.
Try playing with your phone on a flat surface like a table or desk. When you make it to later stages of Easy mode, or any of the stages in Normal or Hard mode, you may want to consider using two hands to hit the triggers on the screen.
On slide triggers, be extra careful not to move your finger outside of the target circle. If you do, you'll watch your hitpoints decrease instead of increase.
If you're interested in levelling-up quickly, purchasing and playing as Lilith will grant a huge boost to your EXP earned per level.