Short answers, pulled from the story.
The first NFL game was played at Douglas Park in Rock Island, Illinois, on the 26th of September 1920. The Rock Island Independents defeated the non-member St. Paul Ideals 48-0 in the new league's opening contest.
The Rock Island Independents played at Douglas Park from 1907 to 1925, including six seasons in the NFL. Their overall NFL record was 26-14-9 across five winning seasons.
Jim Thorpe, Curly Lambeau, George Halas, Paddy Driscoll, George Trafton, Ed Healey, and Jimmy Conzelman all played at Douglas Park. Four of those men played for the Rock Island Independents and were later inducted into the Pro Football Hall of Fame.
The Independents left the NFL after the 1925 season to join the short-lived American Football League. That league folded after its first season in 1926, ending the Independents' existence.
The Rock Island Islanders played minor league baseball at Douglas Park from 1905 to 1937. They were affiliates of the St. Louis Browns in 1932 and the Cincinnati Reds in 1933, and won league championships in 1907, 1909, and 1932.
Yes, Douglas Park is still active. The Quad City 76ers Semi-Pro Baseball Club has played home games there since 1986, and a renovation of the main baseball field reopened on the 9th of May 2017 after the Friends of Douglas Park group raised funds for the project.