Short answers, pulled from the story.
The Vesta family is a group of more than 15,000 asteroids located in the inner asteroid belt, centered on 4 Vesta, the second-most-massive asteroid in the solar system. Most members are small, bright V-type asteroids known as vestoids, formed by a giant impact on Vesta that likely struck its south-polar region.
The Vesta family has more than 15,000 known members. A 2005 search of a proper-element database covering 96,944 minor planets found 6,051 objects within the Vesta family region, about 6 percent of the total surveyed at the time.
HED meteorites are a group including howardites, eucrites, and diogenites that fall to Earth and display basalt-like chemistry resembling planetary rocks. The Vesta family is thought to be their source, with vestoids drifting out of the belt over time and eventually striking Earth as meteorites.
Vestoids are members of the Vesta asteroid family with a V-type spectral signature that links them directly to the surface composition of 4 Vesta. A smaller subset are J-type asteroids, thought to come from deeper layers of Vesta's crust and similar in composition to diogenite meteorites.
Interlopers are asteroids that share the Vesta family's orbital elements by coincidence but lack the V or J spectral signature confirming a genetic link to Vesta. Known interlopers include 306 Unitas, 442 Eichsfeldia, 1781 Van Biesbroeck, and 2086 Newell, identified using the Planetary Data System asteroid taxonomy dataset.
The 1995 hierarchical clustering analysis by Zappala identified 235 core Vesta family members whose proper orbital elements span semi-major axes of roughly 2.26 to 2.48 astronomical units, eccentricities of about 0.075 to 0.122, and inclinations of about 5.6 to 7.9 degrees.