Short answers, pulled from the story.
The present St Paul's Cathedral was designed by Sir Christopher Wren and completed in 1710. Parliament formally declared it complete on the 25th of December 1711, though construction work continued into the 1720s when statues were added to the roof. The first stone was laid in June 1675.
The dome of St Paul's Cathedral rises 365 feet to the cross at its summit. Wren chose this height deliberately, reflecting his interest in astronomy. The cathedral was the tallest building in London from 1710 to 1963.
St Paul's has hosted state funerals for Admiral Lord Nelson on the 9th of January 1806, the Duke of Wellington on the 18th of November 1852, Winston Churchill on the 30th of January 1965, and Margaret Thatcher on the 17th of April 2013. The wedding of Prince Charles and Lady Diana Spencer was held there on the 29th of July 1981, and the cathedral has hosted jubilee thanksgiving services for monarchs including George III, Victoria, George V, and Elizabeth II.
Christopher Wren was the first person interred in the crypt, in 1723. The crypt also holds the tombs of Admiral Horatio Nelson and the Duke of Wellington, as well as memorials to Florence Nightingale, J. M. W. Turner, Arthur Sullivan, Samuel Johnson, Lawrence of Arabia, and William Blake, among many others.
The cathedral was struck by bombs on the 10th of October 1940 and the 17th of April 1941, losing the high altar in the first strike. On the 12th of September 1940, a time-delayed bomb was defused and removed by Royal Engineers under Temporary Lieutenant Robert Davies; had it detonated it would have destroyed the cathedral, and it left a 100-foot crater when remotely detonated elsewhere. Davies and Sapper George Cameron Wylie were each awarded the George Cross.
Wren designed a triple-shell structure to solve two competing visual problems: a dome tall enough to dominate the London skyline would appear oppressively remote from inside the building. The solution is an inner dome visible from the nave, an outer lead-covered dome visible from outside, and a hidden brick cone between them that carries the weight of the stone lantern. The lantern alone weighs approximately 850 tons.