No. Earth's crust does not convect. Convection in the mantle, however can create hot spots and rifting, which can lead tot he formation of volcanoes.

You can conduct it, convect it, or radiate it.

Not within the surface rocks, but at surface level yes. Air and water both convect.

No. The crust is too rigid to convect. The mantle convects, and this convection is part of what controls the movement of tectonic plates.

The much of the mantle is solid but ductile. This allows it to convect, which aids in plate movement.