Short answers, pulled from the story.
Gothic architecture originated in the Ile-de-France and Picardy regions of northern France. The Abbey of Saint-Denis, near Paris, is identified as the first building to bring together the defining Gothic features, with its choir reconstructed between 1140 and 1144.
The term Gothic was applied contemptuously during the Renaissance by those who wanted to revive classical architecture. Giorgio Vasari used the phrase barbarous German style in his 1550 Lives of the Artists, attributing the style to the Goths who sacked Rome, even though the pointed arch has no actual connection to that people.
The defining element is the pointed arch. Its use led directly to the pointed rib vault and the flying buttress, which together allowed builders to construct taller, thinner walls filled with large stained glass windows. These three elements -- arch, vault, and buttress -- are the foundation of the Gothic structural system.
Beauvais Cathedral in France reached a vault height of 48 metres, the highest ever achieved in Gothic construction. A portion of its choir collapsed in 1284, and no cathedral built since has exceeded its height. Only the transept and choir of Beauvais were ever completed.
A series of Gothic revivals began in mid-18th century England, with the two western towers of Westminster Abbey built by Nicholas Hawksmoor between 1722 and 1745 marking an early milestone. Major 19th-century examples include the Palace of Westminster by Sir Charles Barry with interiors by Augustus Welby Pugin, George Gilbert Scott's Albert Memorial in London, and New York's Trinity Church and St Patrick's Cathedral.
Rayonnant Gothic, which emerged in France in the 13th century, maximized stained glass coverage until walls were effectively entirely glazed, as seen in the Sainte-Chapelle completed around 1241-1248. Perpendicular Gothic, unique to England from around the 1320s, replaced curving tracery with straight vertical mullions and horizontal transoms, culminating in fan vaults such as those at King's College Chapel, Cambridge, built between 1446 and 1461.