Short answers, pulled from the story.
Robert Hooke is best known for discovering the law of elasticity in 1660, which he published as Ut tensio, sic vis, and for coining the word "cell" in his 1665 book Micrographia after observing plant structures under a microscope. He also developed the balance spring that enabled portable watches to keep accurate time, and he proposed an inverse square relationship for gravity before Newton formalised it mathematically.
Micrographia, published in 1665, contains the earliest recorded observation of a microorganism, the microfungus Mucor, and introduced the term "cell" for plant structures. It also includes Hooke's conclusion that combustion and respiration both require a specific component of air, observations of fossil wood that led him to argue fossils were the remains of real organisms, and illustrations of the Pleiades star cluster and lunar craters.
In 1686, when Newton's Principia was presented to the Royal Society, Hooke claimed he had given Newton the idea of an inverse square law of gravity, citing a letter he sent Newton on the 6th of January 1680. Newton denied the claim, arguing that Hooke lacked the mathematical demonstrations needed to prove the law, and that without those demonstrations Hooke could only guess it was approximately valid. Edmond Halley reported contemporaneously that Hooke agreed the mathematical derivation of the orbital curves was wholly Newton's.
Hooke designed the Monument to the Great Fire of London in 1672, Montagu House in Bloomsbury and Bethlem Royal Hospital in 1674, the Royal College of Physicians and Aske's Hospital in 1679, Ragley Hall in Warwickshire and the Church of St Mary Magdalene at Willen in Buckinghamshire in 1680, and Ramsbury Manor in Wiltshire in 1681. He also collaborated with Christopher Wren on the design of St Paul's Cathedral and worked on many London churches rebuilt after the fire.
No authenticated portrait of Hooke survives. German antiquarian Zacharias Conrad von Uffenbach reported seeing portraits of both Boyle and Hooke at the Royal Society in 1710, but when the Society moved to new premises later that year, with Isaac Newton as president, Hooke's was the only portrait to go missing and has never been found. Hooke's biographer Allan Chapman rejects as a myth the claim that Newton or his allies deliberately destroyed the portrait.
Hooke argued, against the prevailing theological view, that fossils were the genuine remains of once-living organisms preserved in mineral-laden water over time. He proposed that some fossils represented extinct species, and in a series of lectures in 1668 he argued that the Earth's surface had been shaped by volcanoes and earthquakes, which also explained why shell fossils appeared far above sea level. In 1835, Charles Lyell called Hooke's geological treatise "the most philosophical production of that age" on the causes of change in the natural world.