If an emergency brake fails does that mean the entire brake system is about to fail?

As long as the emergency brake system is not enabled and dragging the brakes, you will be okay to drive the vehicle. The emergency brake system is typically a cable driven system separate from the main fluid driven system. Also make sure the cable isn't disengaged and hanging under the vehicle.

The emergency brake has nothing to do with your brake system. Try to pull the lever back, turn it, and see if it works. Sometimes it doesn't hold, but when you change gears and set it again after parking it will hold. You can reverse with your e brake on, but not move forward.