Short answers, pulled from the story.
The Composite order is a Roman architectural column style that combines the volutes of the Ionic capital with the acanthus leaves of the Corinthian order. It is typically ten diameters high and is considered the most ornate of the five classical orders.
The Arch of Titus, built in 82 AD in the Roman Forum, is the most commonly cited first prominent surviving example of the Composite order. The style is believed to have been invented a little before the reign of Augustus.
Sebastiano Serlio (1475-1554) was the second writer to treat the Composite as an independent order in his book I Sette libri dell'architettura, published in 1537. Leon Battista Alberti had mentioned it earlier, calling it "Italic," but viewed it as a variant of Corinthian rather than a separate order.
At San Carlo alle Quattro Fontane in Rome, begun in 1638, Borromini installed sixteen Composite columns with inverted volutes on the load-bearing columns beneath the arches. This was highly criticised at the time as a violation of the Vitruvian orders.
Renaissance writers deemed the Composite order suitable for churches dedicated to the Virgin Mary and other female saints because of its delicate appearance. More broadly, it came to signal richness and grandeur in both sacred and secular architecture.
The Composite order is not found in ancient Greek architecture. It was a Roman invention and was not ranked as a separate order until the Renaissance, having previously been regarded as an imperial Roman variant of the Corinthian order.