So the only request thats giving me any trouble is retrieve the shell of a man. I'm pretty late in the game and its driving me nuts. I know I have to get in the laboratory and get the anatomical model but its always locked.
You cannot get the anatomical model and bring it to Elizabeth hoping to just do the request as it becomes available (whether because you have three quests already running, or otherwise). You must accept the quest entitled "Retrieve the shell of a man" (#13) and *then* go to the laboratory at the high school.