A friend told me that after the Ark of the Covenant was no longer around that the golden altar of Incense was moved from the holy place into the holy of holies. Did the room remain empty? Was the blood on Yom Kippur then put just on the floor?

Indeed the room remained empty closed with the curtain. The blood was thrown towards the Holy of Holies as if the Ark was still there. (See Mishna, Yoma 53b, Menachot 27b)