Cynthia Cidre, the Executive Producer, didnt see much of the original Dallas (1978) when it aired. But after Warner Bros. hired her to helm the new series, she immersed herself in the old episodes.
Althought Larry Hagman appears in 7 episodes of season 2, he actually passed away during filming of the 5th episode. The Producers managed to keep JR "alive" for two more episodes by rewriting the script and stretching the footage he filmed out with the help of some dialog reused from earlier episodes.
With the beginning of season 3, the show's opening credits properly adopts the style of credits from the original Dallas (1978), i.e. displaying three images of each of the main actors along with their names.
No, this is a continuation of the story from the original TV show. Whereas the original series focused on the bitter fight for control of Ewing Oil between brothers J.R. & Bobby Ewing this new series focuses on their respectives sons, John Ross & Christopher and their new company Ewing Energies.