Let us evaluate all the given statements:

1. Statement 1 is correct: Lanthanoids are silvery-white soft metals. They possess typical metallic structures and are good conductors of heat and electricity .
2. Statement 2 is correct: Actinoids are highly reactive metals, particularly when they are in a finely divided state .
3. Statement 3 is correct: The actinoid contraction is greater from element to element than the lanthanoid contraction. This occurs because the $5f$ electrons provide poorer shielding from the increasing nuclear charge compared to the $4f$ electrons .
4. Statement 4 is incorrect: Many trivalent lanthanoid ions are actually coloured, both in the solid state and in aqueous solutions. This colour is primarily attributed to the presence of $f$ electrons, which allow for $f$-$f$ electronic transitions .