Does the human body use fat to be energetic and heal the immune system, heal cancers and viruses, and make body functions more efficient?

It's source of Ener. Fat just like other 2 main nutrients of our diet(Carbohydrates and Proteins) is a source of energy to run the body machine. It does not have any specific or selective role for the other functions(immunity, healing of cancer etc) that you have listed. In this reference we can be healthy/ normal with small amounts of Fat intake unless you do physical labor requiring extra energy.