Okay, thats a lot of questions.
Admiral: Easy, Flax and the others intend to honour the treaty however the existance of a large Sith Empire can only be percieved as a persistant threat.
The only reason the Republic accepted the treaty to begin with was because it was on the ropes. No Sith is ever going to be trusted by the Republic or the Jedi. THese people aren't planning to betray anyone, they're preparing to be betrayed!
Flax, Sellenna, Hal, Kal, Mirra and Jammes are all Jedi.
Cracken, Redwing: This is simple political theory. The Empire was being controlled by the Apprentice, since the Empire is run through fear and power politics the absense of Cracken and the fact that Starr is running around doing stuff on the ground, not sat on a command chair in an SSD is going to begin to create a power gap.
Over time you would expect the Empire to begin to break down at the edges, as this happened the Republic could pick off these pieces without violating the treaty.
I'm not suggesting that this had happened, just that it was eventually going to and that the Republic was waiting and biding its time.