Statement 1 : Carbon has unique ability to form $\mathrm{p\pi }-\mathrm{p\pi }$ multiple bonds with itself and with other atoms of small size and high electronegativity.

Statement 2 : Heavier elements of group 14th do not form $\mathrm{p\pi }-\mathrm{p\pi }$ bonds because their atomic orbitals are to large and diffuse to have effective sideways overlapping.

Both statements are true.

 Atomic size of carbon is smaller and thus it has effective overlapping with itself and with other atoms of small size and high electronegativity. Few examples of multiple bonding are $\mathrm{C}=\mathrm{C},\mathrm{C}\equiv \mathrm{C},\mathrm{C}=\mathrm{O},\mathrm{C}=\mathrm{S}\mathrm{and}\mathrm{C}\equiv \mathrm{N}.$ Heavier elements do not form $\mathrm{p\pi }-\mathrm{p\pi }$ bonds because their atomic orbitals are too large and diffuse to have effective overlapping.