There were two keys to Arthur's house. Toroko had one of them, and the other one was by Arthur's grave. Why the other was by Arthur's grave is not explained.
As for how Sue got to the Egg Corridor, she probably used the teleporter in Arthur's house. My theory is that King wanted to have Sue ready in case the Doctor was coming again so that he'd take her next time, and that Toroko, knowing this, had Sue go into Arthur's house and then locked the door after she went in so that King couldn't get to her. This theory is based on the fact that when you first arrive, King wants to get to Sue, and apparently knows he has to get into Arthur's house to do so. And he also seems to know that Toroko has the key. And judging by the fact that Toroko is trying to keep the key from King, she probably helped Sue get in.