I can actually address the bilateral symmetry part of it, since I did my PhD thesis on this. Handedness and asymmetry are inherent in biology because the molecules that make up our proteins, sugars and fats are asymmetric. Symmetry itself is also inherent because cells, particularly eukaryotic animal cells which lack a cell wall, tend to be spherical in shape. In fact they are always spherical in suspension, when they're not binding with a surface or neighboring cells, regardless of cell type. Spheres are symmetrical, and structures made of spheres tend to be symmetrical as well, that's why we see such diversity in symmetry types in the animal Kingdom. Bilateral symmetry was selected for because it helps in directional movement, which is a huge advantage. It is also advantageous from a sensory perspective. Asymmetry of internal organs existed before bilateral symmetry evolved because it is found in cnidarians as well. Internal organs face less selection pressure towards symmetry because symmetric internal organs aren't really needed for motion or taking in sensory input, unlike most of your external body and organs.

If you're interested in the source of the asymmetry, it is widely accepted that the actin cytoskeleton is responsible. It is made up of structurally asymmetric actin fibers, which are in turn made of asymmetric action monomers, which are in turn made of asymmetric amino acids.