When the contract is signed, there is the housing transfer (Wohnungsübergabe). You get the key, go through the apartment again and at this point (at the latest), you write about the condition of the apartment. So that you both know whether the apartment is completely renovated or the apartment should be renovated by the landlord. It should all be noted on the protocol. If there are still broken things and they should be repaired then you need to write these things down in the protocol. In addition, the meters for electricity and gas are recorded so that everything is ready at the time the apartment is occupied. Also the meters on the electricity and gas should be noted so that you when you move in, everything will be fixed and ready. Both you and the landlord should have a copy of the protocol.
This is the same if there is still furniture inside. If the last tenant says that you can keep the furniture then it does not have anything to do with the apartment or the landlord. But that is an agreement between you and the previous tenant. This means that you have to take care of the furniture when you move out. Apart from that, you also have the right to get furniture money from the LAF or Jobcenter. As soon as the lease contract is made, you can apply for “Antrag auf Erstausstattung der Wohnung” which means that you can get furniture and household equipment when you first move in.