Short answers, pulled from the story.
Classical architecture refers to building traditions consciously derived from the principles of ancient Greek and Roman architecture, particularly from De architectura, written by the Roman architect Vitruvius around 10 AD. Its decorative and structural elements form a shared vocabulary that architects have adapted and reinterpreted from the Renaissance onward.
Petrification, sometimes called petrified carpentry, describes the process by which ancient Greek builders copied the shapes of earlier wooden temple structures when they transitioned to dressed and polished stone during the Archaic and early Classical periods (roughly the 6th and early 5th centuries BC). The wooden forms were preserved so faithfully in stone that scholars believe religious obligation, rather than aesthetics, may have driven the practice.
Vitruvius was the Roman architect who wrote De architectura around 10 AD, the single most influential treatise on classical architectural principles. Renaissance architects including Leon Battista Alberti, Sebastiano Serlio, and Giacomo Barozzi da Vignola used it as a primary source when attempting to revive ancient Roman architecture in Italy.
Leon Battista Alberti, Sebastiano Serlio, and Giacomo Barozzi da Vignola led the Renaissance effort to revive ancient Roman architectural language. Filippo Brunelleschi is also central to this period; his Ospedale degli Innocenti in Florence, built between 1419 and 1445, is among the earliest Renaissance buildings.
Neoclassical architecture emerged around 1750 as a reaction against Baroque and Rococo styles, aiming to return to the principles of ancient Greek and Roman building with greater rigor and rationality. It held a strong position on the architectural scene from roughly 1750 to 1850; early theorists included Claude Perrault, Marc-Antoine Laugier, and Carlo Lodoli.
Andrea Palladio, a Venetian architect who lived from 1508 to 1580, developed a style that became especially influential in Britain long after his death. Palladian architecture was adopted for many of the grander buildings of Georgian Britain during the 18th and early 19th century.