Short answers, pulled from the story.
The Paleogene Period is the first period of the Cenozoic Era, spanning 43 million years from the end of the Cretaceous Period to the beginning of the Neogene Period. It is divided into three epochs: the Paleocene, the Eocene, and the Oligocene. The period is often abbreviated as Pg.
The Paleocene-Eocene Thermal Maximum was triggered by volcanic intrusions into organic-rich seafloor sediments in the North Atlantic Igneous Province between roughly 56 and 54 million years ago, which rapidly released large amounts of greenhouse gases. Global mean surface temperatures reached 31.6 degrees Celsius. A study published in 2018 found that annual air temperatures over land at mid-latitudes averaged about 23-29 degrees Celsius from roughly 56 to 48 million years ago, some 10-15 degrees above current values in those regions.
The global boundary marker for the base of the Paleogene is at Oued Djerfane, west of El Kef in Tunisia. It is identified by a rusty-colored clay layer 50 centimeters thick that contains an iridium anomaly, microtektites, nickel-rich spinel crystals, and shocked quartz, all indicators of the asteroid impact whose crater remnants are at Chicxulub on Mexico's Yucatan Peninsula.
Mammals diversified rapidly from a few small, generalized survivors of the Cretaceous-Paleogene extinction event into most of the modern orders seen today. Some lineages evolved into large land-dwelling forms, others returned to the ocean and became cetaceans and sirenians, and others took to trees, giving rise to groups including primates, the group to which humans belong.
The opening of the Drake Passage between South America and Antarctica, and of the Tasmanian Passage to the south of Australia, established the Antarctic Circumpolar Current during the Paleogene. This current isolated Antarctica in cold polar waters, drove dense polar water into the deep ocean, and reduced global temperatures. By roughly 37 million years ago there is evidence of glaciation in Antarctica, and by the Eocene-Oligocene boundary an ice sheet had formed in western Antarctica extending to the ocean.
Around 48.5 million years ago, a proliferation of aquatic ferns from the genus Azolla across the Arctic Ocean sequestered large amounts of atmospheric carbon dioxide, ending the warm early Eocene conditions. This Azolla event initiated a slow cooling trend, the Middle-Late Eocene Cooling, that lasted from about 48.5 million years ago until roughly 34 million years ago.