If I don't want the furniture that is in the furnished apartment and my landlord won't remove any of it, can I place it in storage?
Question Details: And, if so, who covers the cost?
If you rented a furnished apartment--that is, you rented it knowing it was furnished--you cannot remove or store the furniture unless the landlord gives you permission to do so, and the landlord could require you to pay any moving and storage costs for so doing. That is because in this case, you rented the apartment knowing it was furnished, or subject to it being furnished, and you take the apartment in the shape, and with the furniture and appliances, it was in when you agreed to rent it.
If you did not intend to rent a furnished apartment and did not agree to rent a furnished one, then you could require the landlord to remove the furniture and pay the cost thereof--when you rent an unfurnished space, the landlord may not choose to put his/her belongings into it.