Short answers, pulled from the story.
An Earth mass is a unit equal to the mass of the planet Earth, approximately six ronnagrams. Astronomers use it to express the masses of other planets and exoplanets; for example, Jupiter is 317.8 Earth masses and the Sun is about 332,946 Earth masses.
The first measurement within about 20% of the correct value came from the Schiehallion experiment in the 1770s, organized by Astronomer Royal Nevil Maskelyne. Henry Cavendish in 1798 then measured the gravitational constant directly in a laboratory, arriving at a mean density only about 1% below the modern value.
Iron and oxygen each account for roughly 32% of Earth's mass. Magnesium and silicon each contribute about 15%, while calcium, aluminium and nickel each contribute about 1.5%.
Measuring Earth's mass requires measuring the gravitational constant G, which is the fundamental physical constant known with the least accuracy due to the relative weakness of gravity at laboratory scales. High-precision measurements from the 1980s to 2010s have yielded mutually exclusive results.
Yes, Earth experiences a net mass loss estimated at roughly 5.5 times ten to the seventh kilograms per year. About 100,000 tons per year is lost through atmospheric escape of hydrogen and helium, while around 45,000 tons per year is gained from infalling cosmic dust and meteorites.
Charles Hutton's 1778 analysis of the Schiehallion results suggested for the first time that Earth's interior must be substantially composed of metal, not ordinary rock. Hutton estimated the metallic portion occupied about 65% of Earth's diameter, close to the modern value of 55%.