Short answers, pulled from the story.
Breakthrough Initiatives was founded in 2015 and announced to the public on the 20th of July 2015 at London's Royal Society by physicist Stephen Hawking. It was created by Russian tycoon Yuri Milner and is funded by Julia and Yuri Milner, who also fund the Breakthrough Prize.
Breakthrough Listen, a project of Breakthrough Initiatives, searches for artificial radio or laser signals from more than a million stars and the centers of 100 galaxies. It has $100 million in funding, began in January 2016, and is expected to run for 10 years.
Breakthrough Starshot, a project of Breakthrough Initiatives, aims to send its spacecraft fleet toward Alpha Centauri at about 20% the speed of light, or 60,000 kilometers per second, roughly 215 million kilometers per hour. At that speed the journey would take about 20 years, plus about 4 more years for a signal to reach Earth.
Pete Worden is the head of Breakthrough Starshot, the Breakthrough Initiatives program announced on the 12th of April 2016 to develop a light sail spacecraft fleet with a US$100 million budget.
Breakthrough Message, part of Breakthrough Initiatives, studies the ethics of sending messages into deep space and ran an open competition, with a US$1 million prize pool, to design a message representative of humanity and planet Earth. The program has pledged not to transmit any message until there has been a global debate on the risks and rewards of contacting advanced civilizations.
NASA signed a collaboration agreement with Breakthrough Initiatives in September 2018 to jointly develop the Breakthrough Enceladus mission concept. If launched, it would be the first privately funded deep space mission.