The fighting style that Major Sheppard and Teyla are practicing is a Filipino martial art called escrima.
In the opening scene, you can see an Amazing Avenger comic book next to Lt. Ford's bed. This is the superhero mentioned by Dr. Jay Felger; he says he read comic books as a young boy, and this was the inspiration for the name of the Avenger virus in the Stargate SG-1 (1997) episode Avenger 2.0 (2003).