Short answers, pulled from the story.
A morpheme is the smallest lexical item or unit of meaning in a language. It describes the invisible architecture that holds all human language together and serves as the smallest meaningful constituent within a linguistic expression.
Free morphemes, such as the words town or dog, possess the autonomy to stand alone as complete words. Bound morphemes are linguistic units that cannot exist independently and must always attach themselves to a root to gain any meaning or existence.
Derivational morphemes, such as the suffix -ness, change the part of speech of a root to create a new word. Inflectional morphemes modify the tense, aspect, mood, or number of a word without changing its fundamental class, and English utilizes eight distinct inflections.
Allomorphs are multiple forms of a single morpheme that manifest depending on the phonological environment of the root. Zero-morphemes convey meaning without any physical sound, such as the null plural suffix in the word sheep.
Content morphemes include free morphemes like nouns, adverbs, adjectives, and main verbs that express tangible reality. Function morphemes operate as the glue that holds sentences together, including prepositions, pronouns, determiners, and auxiliary verbs that connect ideas grammatically.
The definition has shifted from simple lexical units to complex features that interact with syntactic trees and semantic structures. Distributed morphology and radical minimalism propose that leaves in syntactic trees spell out morphemes or even smaller nano-morpho-syntactic features.