How do neutral solutes move across the plasmalemma ? Can the polar molecules also move across it in the same way ? If not, then how are these transported across the membrane? 
The neutral solutes move across the plasma membrane by simple diffusion. They diffuse across the membrane along their concentration gradient that is from their higher concentration to their lower concentration.

Passage of polar molecules : Due to bilayer of nonpolar lipid molecules, the polar molecules cannot pass through biomembranes. They require carrier molecules to facilitate their transportation across membrane. The transport of certain molecules takes place against their concentraion gradient from lower to higher concentration, this process requires energy and is an active transport process. The energy is provided by ATP.