1) Yes, there is carpet in the room.
2) Yes, there is a window in the room.
3) No, there is one table in the room.(исправь у себя в вопросе ARE there)
4) No, there is two armchairs in the room. (не вижу, вроде там 2 кресла)
5) Yes, there is a sofa in the room. (исправь у себя в вопросе IS there)
6) Yes, there is a lamp in the room.
7) No, there is no bookcase in the room.
8) Yes, there is a one picture in the room. (допиши у себя are THERE)