Does the world know that the Justice League and Avengers were separate until 2001 or were they merged since their origin?
As far as the world is concerned both teams were separate from each other from the moment of their creation (around 1989) till 2001. The reason why both teams joined forces was explained by the Spectre in JLA #1; to prevent another event like the Merge from ever happening the most powerful members from each team joined forces under one banner. This was explored more in JLA #2 through a series of flashbacks. One showed Diana moving to Avengers Mansion while another showed Tony and J’onn looking over as workers rebuilt it into its current incarnation, the Hall of Justice.
