Short answers, pulled from the story.
The thickened layer of skin surrounding fingernails and toenails carries the medical name eponychium. Medical professionals use this term to describe the cuticle in general parlance.
Arthropod cuticles rely primarily on chitin as their main structural component. Chitin is a polysaccharide composed of N-acetylglucosamine units that become cross-linked with proteins within the exoskeleton.
Cuticles function as permeability barriers for both water and water-soluble materials by preventing plant surfaces from becoming wet during heavy rain events. This barrier helps keep internal moisture levels stable under harsh conditions.
Water beads up and runs off the leaf of Hosta sieboldiana because the epicuticular wax covering creates a hydrophobic surface that resists wetting completely. Extreme resistance to wetting depends largely on microscopic shape rather than just chemical coating.
The outer layer of tissue forms one term used for mushroom basidiocarp structures while the alternative term pileipellis means skin of the cap in Latin language. The pileipellis or peel remains distinct from the inner fleshy trama tissue and differs from the spore-bearing tissue layer called the hymenium.