Where is the Salty Oyster

The key unlocks a chest in a house called the "Lansdowne Residence." You'll find this location from backtracking out of the Order of the Raven, over a skyhook grapple point, and through either a double doors or a skylight into a bedroom.

From the bedroom, go down two flights of stairs to the middle level. There's another bedroom and a bathroom on this floor, and the chest is in the bedroom.

In the chest is a salt recovery item and an infusion. There's also a voxophone in the room which explains why the chest (but not the key) is in the house.

Potential spoilers below.

Rosalind says that it's probably because part of Elizabeth exists in another universe (her cut pinky), and thus can interfere with the tears/make new ones.

The actual quote: "What makes the girl different? I suspect it has less to do with what she is and more to do with what she's not. A small part of her remains from where she came. It would seem the universe does not like its peas mixed with its porridge."

As for the Luteces, when Fink sabotaged their tear machine to kill them, it somehow caused the siblings to be able to travel through tears freely, which is what they do throughout the game.