1. I live in Dalian, south of China
Not really. 'South of x' means that somewhere is located to the south of x. For example, 'Vietnam is south of China', meaning that it is in a more southerly location. You could say 'I live in Dalian, in the south of China', however.
2. I live in Dalian, southern China
Yes, this is fine.
3. I live in Dalian, south China
Again, not really. South is not an adjective. The only time you can put 'south' before a place name is when it is capitalised, and part of the official name of that place, for example 'South Korea' or 'South Africa'.
Sorry, but sentences 4 5 and 6 are very confusing, because it isn't clear what language point you are asking about. There are too many possible combinations of meanings.