Short answers, pulled from the story.
Evidence suggests life emerged before 3.7 Ga, the age of biogenic carbon signatures and stromatolite fossils found in metasedimentary rocks from western Greenland. Earth itself formed about 4.54 billion years ago, give or take 50 million, and the oceans had formed by 4.4 billion years ago. Disputed evidence from the Nuvvuagittuq Belt in Quebec, Canada, suggests microorganisms may have lived as early as 4.28 billion years ago.
The Great Oxygenation Event was the buildup of free oxygen in Earth's atmosphere around 2.4 Ga. It happened after cyanobacteria evolved photosynthesis around 3.5 Ga and free oxygen saturated all available reductant substances on Earth's surface. Oxygenic photosynthesis raised biological productivity by a factor between 100 and 1,000.
Eukaryotes arose through a sequence of endosymbiosis between prokaryotes, a conclusion reached in a vigorous 1970s debate. A predatory microorganism invaded a large prokaryote, probably an archaean, and evolved into mitochondria, while a later swallowed cyanobacterium became the ancestor of plants. The earliest evidence of eukaryotes dates from 1.85 Ga.
The leading hypotheses include the RNA world, where replication came first because some RNA molecules catalyze their own replication, a lipid world where membranes formed first, a clay hypothesis centered on montmorillonite, and an iron-sulfur world where metabolism came first. Research focuses on three starting points: self-replication, metabolism, and external cell membranes. Evidence suggests the first RNA molecules formed prior to 4.17 Ga.
Sexual reproduction is a puzzle because an asexual population can out-breed and displace an otherwise equal sexual population in as little as 50 generations. Competing explanations include the Red Queen hypothesis about parasites and Alexey Kondrashov's deterministic mutation hypothesis, but each faces contrary evidence. The red alga Bangiomorpha, dated at 1.2 Ga, is the oldest known sexually reproducing organism.
Mass extinctions accelerated evolution by eliminating dominant groups and making way for new ones, rather than because the newcomers were superior. The Permian-Triassic extinction event wiped out almost all land vertebrates, and during a recovery estimated at 30 million years the archosaurs and then dinosaurs rose. After the Cretaceous-Paleogene extinction killed the non-avian dinosaurs, mammals increased rapidly in size and diversity.