These hearts are sometimes(rarely) dropped by enemies(some enemies don't drop them at all). They can be found throughout the game and they refill one heart of life. They can also be found in groups.
These stars are dropped by enemies more often than the hearts. If you collect five of these stars, it will refill one heart of life. The star on your in-play menu will show the amount of stars you currently have.
You can find these bottles of medicine in hidden rooms throughout the game. They refill some of your life, or all of it if you have a low amount of heart containers. To use the collected medicine, press PAUSE, then UP on the d-pad, and select the medicine.
Collecting these tetrads are the whole reason Mike it traveling through Time. You'll find one at the end of each Chapter.
Chapter 2 Weapons
In this game Mike doesn't have his yoyo.. so the first thing you pick up as a weapon is a pile of rocks.
This is the first real weapon you get in the game. You come accross a cave of cave-people, and one of those people is a weapons maker named Tink. He gives you the axe for free.
For the unknowning, Tetrads are actually game pieces from the game Tetris.