Klo is short for Klosett, which is, if cleaned with water, a water closet, hence WC. So if it hasn't a water flushing, I wouldn't call it 'WC', but 'Klo' or 'Toilette'. All 3 words are used to describe the furniture as well as the room.
A 'Bad' is the room where the 'Badewanne' is located, and in most households, the bathroom contains a closet, but it needn't, and in a restaurant, or a public building like a library or a shopping mall, there is normally no bath or shower in the room, so you don't ask for a 'Bad' there.
'Klo' is a bit simple, so you ask for Toilette or WC when talking to strangers. In the family, or with close friends, 'Klo' is alright.