Air conditioner is a device Air condition is a process that used to cool (or rise the temperature of the air) the air

There is a verb "air-condition", but it is seldom used, in my experience. People once referred to air-conditioners, window units used for cooling a living space, but now modern homes enjoy central heating and air-conditioning. Note that "air-conditioning" means only cooling in English, whereas in Chinese one word means both heating and cooling（空调）.

Neither! In general use, it's Air Conditioning. 'It's too hot in here, the air conditioning doesn't work'. If you want to talk about the specific machine, you'd have to say air conditioning machine, or perhaps air conditioning system. air conditioner sounds like a sensible name for the device, but no-one actually says it. air condition is not used, unless you are writing a technical article about pollution. nb. This is UK English, I guess it might be different in countries where they actually need air conditioning:-)

When people are talking about the machine, they call it an air-conditioner. ("My air conditioner is broken, so I had to buy a new one." "How much does that air-conditioner cost?") When people are talking about a building, they might talk about whether it has air-conditioning, as a kind of service. ("This is a nice apartment. Does it have air-conditioning?" "Does the hotel have air-conditioning?")