Dimensionality often strongly affects material properties and phase transition behaviors, but its effects on crystal surfaces, such as roughening and premelting, have been poorly studied. Our simulation revealed that these surface behaviors are distinct in monolayer and multilayer Lennard-Jones (LJ) crystals. Solid surfaces fluctuate as capillary waves during the roughening process, but complete roughening is preempted by premelting. As the melting temperature is approached, the thickness of the premelted liquid layer approaches a constant (i.e., blocked premelting) for monolayer crystals, but diverges as a power law (i.e., complete premelting) for bilayer and trilayer crystals. The surface liquids of monolayer crystals contain crystalline patches and exhibits rough liquid-vapour and liquid-crystal interfaces, in contrast to the normal surface liquids of bilayer and trilayer crystals. Monolayer crystals melt heterogeneously from the surface without forming a hexatic phase and produce many vacancies.