Immediately after the intro sequence, Daniel's desk is shown with a picture of James Spader, who portrayed Daniel Jackson in Stargate (1994).
When Jack says, "We'll do it! It's what we do, isn't it?" it's reminiscent of Nick Marlowe's "Hey! It's what I do." from Stargate SG-1 (1997) Wormhole X-Treme! (2001).
Carter's reactions regarding the loss of Daniel are at odds with a military professional. Anyone in the military, especially in front line units, has to be able to accept the loss of a comrade, even one they've been with for years. If Carter can't accept this and put it behind her, she has no place in the military. Harsh as it seems, it is just a fact of life in the military.