In the posture where the palms are facing the earth, the instruction is to align with the earth. What does that mean? Are we to feel qi moving up into the palms of the hands from the earth; or old qi moving out of the palms, downward into the earth?

The Earth's energy is gravity. So, you are lining your body with the force of gravity, feeling a connection with the Earth. You can also, feel the energy of the Earth in your hands. It's simple to start with, you don't have to send energy out the hands and exchange it with the Earth, just line up your body, feel the Earth and then get ready for the next posture.