Can someone explain "Saw 4"?

i dont get what the third killer (leiutenant) had to do with jigsaw or amanda. or why and what that letter sed when amanda opend it and started crying. when did the autopsy of jigsaw happen? was it before officer rigg found out who the third killer was or afterwards? but then agen after officer rigg got shot, the third killer procceded to go shut the door to the room ofjefffrom saw 3, amanda,AND jigsaws FRESH dead corpse. and i believe at the end of saw 3, the tape that jigsaw played after he died sed jeff hadn't killd jigsaw because he's the only person that knows where his daughter is and the oonly way to get her back is to play a game....what was the game? theres lyk alot of holes in saw 4 unless im just not getting it.