Short answers, pulled from the story.
The word concerto comes from the Italian, meaning accord or gathering. It derives from the Latin verb concertare, which indicates a competition or battle. The dual meanings of cooperation and contest reflect the form's central dynamic between soloist and ensemble.
Compositions were first indicated as concertos in the title of a music print when they were published in 1587. These early concertos were vocal works, not instrumental pieces.
Corelli's concertino group consisted of two violins, a cello, and basso continuo. He developed the concerto grosso form in the late Baroque period, which placed this small group in dialogue with a larger ensemble.
Mozart wrote 27 piano concertos. The last 17 are particularly highly regarded. He also arranged keyboard versions of works by other composers as a child.
Beethoven's violin concerto remained obscure until violin virtuoso Joseph Joachim performed it on the 27th of May 1844, revealing it as a masterpiece.
The Concerto for Group and Orchestra was a concerto written for a rock band, performed by Deep Purple. It is one of the most unusual examples of the form, placing a rock ensemble in the role normally occupied by a classical soloist.