Short answers, pulled from the story.
The Global Carbon Project began its work in 2001 as a formal partnership among four major international science programs. These founding groups included the International Geosphere-Biosphere Programme, the World Climate Programme, the International Human Dimensions Programme, and Diversitas.
The organization established the Global Carbon Budget as an annual publication tracking global carbon sources and sinks starting in 2005. Each year the team revised and updated data along with changes in analysis or results to present a synthesis where results from individual groups were collated and evaluated for consistency.
Fossil CO2 emissions reached a record 37.1 billion tonnes in 2018 according to the project's December 2018 report. This represented a rise of 2.7% compared to the previous year with a range between 1.8% and 3.7% driven by increases in global use of natural gas and oil.
The organization released its newest Global Methane Budget and first Global Nitrous Oxide Budget in 2020. These two anthropogenic trace gases were identified as most dominant for warming after carbon dioxide, allowing scientists to assess collective national climate progress using methods estimating differences in emissions from land-use change.
Rob Jackson of Stanford University currently chairs the organization while Josep Canadell serves as executive director from Australia's Commonwealth Scientific and Industrial Research Organisation. The project maintains international offices in Tsukuba Japan and Seoul Korea alongside an international scientific steering committee consisting of a dozen scientists representing five continents.