Short answers, pulled from the story.
A comet nucleus is a loose collection of rock, dust, water ice, and frozen carbon dioxide, carbon monoxide, methane, and ammonia. It also contains organic compounds such as methanol, hydrogen cyanide, formaldehyde, ethanol, and ethane. Fred Lawrence Whipple described comets as "dirty snowballs" in 1950.
Comet nuclei range from a few hundred meters to tens of kilometers across, with some observed up to 30 kilometers in radius. The coma can grow thousands or millions of kilometers wide, up to 15 times Earth's diameter, and the tail may stretch beyond one astronomical unit.
Short-period comets originate in the Kuiper belt and its associated scattered disc, beyond the orbit of Neptune. Long-period comets are thought to come from the Oort cloud, a spherical cloud of icy bodies extending halfway to the nearest star and holding about one trillion comet-like bodies.
A comet's tail forms when sunlight vaporizes material from the nucleus as it nears the Sun, a process called outgassing. Radiation pressure pushes dust into an arcing dust tail, while the solar wind drives ionized gas into an ion tail that points directly away from the Sun.
In 1705, Edmond Halley applied Newton's method to 23 cometary apparitions between 1337 and 1698 and found that the comets of 1531, 1607, and 1682 shared similar orbits. He predicted the same comet would return in 1758 to 1759, and three French mathematicians later refined the date to within a month.
Yes, the European Space Agency's Philae lander touched down on Comet Churyumov-Gerasimenko on the 12th of November 2014, the first time a spacecraft had ever landed on a comet. It was carried there by the Rosetta probe and found at least sixteen organic compounds at the surface.
Yes, three objects have been found with eccentricity significantly greater than one, indicating an interstellar origin: 1I/ʻOumuamua, 2I/Borisov, and 3I/ATLAS. 2I/Borisov, with an estimated eccentricity of about 3.36, has a coma and is considered the first detected interstellar comet.