Princess Heart:
When you start the mine mini-game, choose the grey door on the upper left. Continue north thru a door. Then take the door on the right. Then take the door on the left. If you continue on this path, you'll get to an area with a glowing red outline.
The red-outline-area connects to a bunch of dead-end rooms, and one of them has the heart. You'll know you've found the right room if you find a chamber with grey mine floor and an item in the center in something that resembles a mine-cart.
Blue Face:
In the Forest (Flower) Zone, in the tree stump just south of the statue room, is a coffin that requires 2 bones to open. The first bone is located on the very second screen from Uratheul's original entrance. The second bone is in a safe in the Snake Zone.