A Pesky Propaganda
On the matter of the key, you find only that no locksmith knows of, or can even conceive of a lock it would open.
Researching the bandages you discover the booming funeral business, since death is rarely permanent, but frequently disfiguring, old and badly hurt members of society are encouraged to head to the Tomb Colonies, where they are surrounded by other members of the nearly dead. When in the Capital, it is considered polite to wrap oneself in bandages to cover any rotting flesh, disfiguring scars, or missing body parts, and most are happy to do so. Members of the Tomb Colonies are otherwise usually treated as dead, and funerals are often held with the “deceased” sitting in a chair, rather than a coffin, and they will make a speech before being wrapped in their first bandages
On the matter of divination you find that arcane magic of any source is not rare, but less common than on the surface, the only option anyone has recommended to you is the gypsy fortune teller Madame Shoshana, though there is also a group of Mediums who regularly perform sermons at Mahogany Hall.
Choose one of these things to get more information on come game day.