Short answers, pulled from the story.
A day on Earth averages 24 hours, or 86,400 seconds. In the International System of Units the day carries the symbol d and is defined as exactly 86,400 seconds, though Earth's actual rotation introduces small variations.
A solar day is the time for the Sun to return to its highest point in the sky, averaging about 24 hours, while a sidereal day measures one full rotation relative to a distant star and runs about four minutes shorter at 23 hours, 56 minutes, and 4.09 seconds. There are about 365.2421875 solar days in a mean tropical year and about 366.2422 stellar days, one more than the count of solar days.
The day is lengthening mainly because of tidal deceleration, as the Moon's gravitational pull slows the Earth's rotation. The mean solar day now lasts about 86,400.002 seconds and grows by roughly 2 milliseconds per century, and at the Earth's formation a day is estimated to have lasted only 6 hours.
A leap second is an extra second inserted into Coordinated Universal Time to keep clocks in step with the slowing Earth, making a civil day 86,401 or 86,399 SI seconds long instead of the usual 86,400. From 1972 through 2022 a total of 27 leap seconds were added, roughly one every other year, and the International Earth Rotation and Reference Systems Service announces each one in advance.
The convention varies widely. The Jewish day begins at sunset or nightfall when three second-magnitude stars appear, ancient Egypt reckoned the day from sunrise to sunrise, and the ancient Romans, ancient Chinese, and modern practice begin the civil day at midnight. Astronomers traditionally started a day at noon so a single night's observations fall on the same date.
Paleontologist John W. Wells estimated ancient day lengths by measuring sedimentation rings in coral fossils, since some biological systems are affected by the tide. By this method the Cambrian held about 425 days per year of 20 hours and 40 minutes, while the Cretaceous had about 380 days of 23 hours and 20 minutes.