Answer to Question 1
If the heat leaving Earth was coming from the crust, we should see higher heat flow values on continental crust than oceanic crust because the continental crust is thicker and it contains more radioactive elements. This is the opposite of what is actually occurring.
Answer to Question 2
Chemical convection is motion of material that is caused by density differences due to different chemical compositions. At the surface of the inner core, solid iron is crystallizing from the liquid outer core, resulting in a lower-density, iron-depleted liquid that will rise up to start the convection cycle.