Question: How was Elijah getting out of his room in the first place? I know he has free roam of the facility after killing the guard and taking his keycard, but I don't recall the movie explaining how he was getting out earlier in the movie?
Answer: At one point, Elijah's mother mentions that he caught a glimpse of and instantly memorized a blueprint of the psychiatric hospital when he was first committed, and he used that knowledge to short-out the hospital's electrical system one time (before they started heavily sedating him). It seems likely that Elijah was able to somehow hotwire electronic door locks, using his knowledge of the hospital's electrical system. Later, he used a master keycard taken from the guard.
Answer: Not only that but, it was shown in the first movie that Elijah was very good at manipulating people so he could have convinced somebody to let him out.
Answer: The movie doesn't explain. But given what we know about Elijah from "Unbreakable" and this film, it's really no surprise he managed to find a way out - he's psychotic, but he's also a genius.
Answer: He's picking the locks on the doors, bypassing the keycards.