I am wondering whether there is a federal statute or case law that discusses tenant rights to privacy? For example, a landlord enters a person apartment without their knowledge and one of the landlord's agents steals money.
Theft is of course illegal in all US states, and pretty much every other jurisdiction. In the US that is a matter of state law, not federal. It could be reported to the local police, but it might be hard to prove.
Both landlord/tenant law and privacy law are largely matters of state law in the US, not federal law. Such laws vary a good deal in different states. In many states a landlord is allowed to enter the rented premises, usually on "reasonable" notice, or without notice if there is an emergency. If the landlord actually lives in another part of the house, and simply rents a room to the tenant, the landlord may be able to enter the room more freely than if it was a separate apartment or house.
In many cases where there is a written lease or rental agreement, it will specify under what conditions the landlord or landlord's agent may enter, and how much notice is required. What does the lease in the current case say about that?