Short answers, pulled from the story.
Berkelium was first intentionally synthesized, isolated, and identified in December 1949 at the University of California, Berkeley. Glenn T. Seaborg, Albert Ghiorso, Stanley Gerald Thompson, and Kenneth Street Jr. created it using the 60-inch cyclotron at the Lawrence Radiation Laboratory.
Berkelium is named after the city of Berkeley, California, following the tradition of the Berkeley research group of naming new actinide elements in analogy with the lanthanide element positioned above them in the periodic table. Berkelium's lanthanide analogue is terbium, whose name derived from the town of Ytterby, Sweden, so element 97 was similarly named after a city.
Just over one gram of berkelium has been produced at Oak Ridge National Laboratory since 1967. During the period 1967 to 1983 alone, only 0.66 grams were made. Berkelium-249 costs on the order of 185 US dollars per microgram.
A 22-milligram batch of berkelium-249 was prepared during a 250-day irradiation at Oak Ridge in 2009, then purified for 90 days and shipped to the Joint Institute for Nuclear Research in Dubna, Russia. There it was bombarded with calcium-48 ions for 150 days, yielding the first six atoms of element 117, tennessine.
The most important isotope for production and research is berkelium-249, which has a half-life of 330 days. The longest-lived isotope is berkelium-247, with a half-life of 1,380 years. Berkelium-248 is estimated to have a half-life in excess of 300 years, though its exact value is uncertain.
Berkelium is produced primarily at two facilities: the 85-megawatt High Flux Isotope Reactor at Oak Ridge National Laboratory in Tennessee, USA, and the SM-2 loop reactor at the Research Institute of Atomic Reactors in Dimitrovgrad, Russia. Both are dedicated to producing elements with atomic numbers above 96.