Short answers, pulled from the story.
Sailors named the Barents Sea the Devil's Dance Floor because of its extreme unpredictability and difficulty. Ocean rowers also call it the Devil's Jaw; in 2017, after the first recorded complete man-powered crossing from Tromsø to Longyearbyen, expedition captain Fiann Paul described the winds as like breath from the devil's nostrils while the sea holds a rower in its jaws.
The Barents Sea was named after Willem Barentsz, a Dutch navigator and explorer who led expeditions to the far north at the end of the 16th century. Before Europeans gave it that name, Russians called it Murmanskoye more, a name that remained in official use until 1853.
Norway and Russia signed a boundary agreement in 2010, placing the border equidistant from each country's original claim. The agreement was ratified and came into force on the 7th of July 2011, resolving a dispute that had been under negotiation since 1974 and opening a 175,000-square-kilometre grey zone to hydrocarbon exploration.
The Shtokman field is a giant gas field discovered in 1988 in the Russian sector of the Barents Sea. It is currently ranked as the 5th-largest gas field in the world.
Scientists describe the Barents Sea as the Arctic warming hot spot because rising temperatures have reduced sea ice and weakened the stratification of the water column. As the permanent ice-free area grows, increased evaporation is predicted to drive greater winter snowfall across much of continental Europe.
Fishing is managed jointly through the Joint Norwegian-Russian Fisheries Commission, established in 1976. The Commission sets Total Allowable Catches for multiple species and facilitates the exchange of quotas and catch statistics between the two countries, though under-reporting by fishing vessels remains a significant problem.