The financial markets is simply reacting to the Chinese economic numbers as they are released confirming that the economy continues to slow. It also suggest that the various measures taken by the Chinese central government in recent times are not having the desired effect to jump start the economy. Discounting the connection of the Chinese economy to the Chinese stock market and the correlation is missing the point. It is true that not all stock market downturn precedes an economic slowdown or recession. However the historical empirical evidence are there to support the view that all major economic downturn are preceded by similar stock market movements by between 12 to 18 months.
The reasons for such a correlation is actually easy to understand and intuitively self evident. In a rising stock market, companies enjoy a healthy economy with consumer spending driving company profits due to demand. The increasing profits are reflected in enhanced market valuation as evident by increasing PE's. This obviously in turn drive stock prices upwards. When the economy turns, the reversal of fortune starts to take a similar effect on company profits which is reflected in depressed earnings and hence valuation and consequently on stock prices. The major point to note is that in a western type market where market information is efficient, smart money starts to rebalance their portfolio ahead of the general crowd and hence there is always a lag between the economy and the stock market with the latter leading the way by at least 12 months. In the Chinese stock market, institutions are not as heavily weighted and so the correlated pull and effect might be different but the principles remain unchanged. The higher volatility of the Chinese stock market in my view is attributed to basically three things. Firstly it is just one big Chinese casino and investment decisions tend to be generally speculative based on rumours and greed. Secondly, market information is not as efficient and so reactions of market participants tend to over-react when dealing with rumours because of the lag in official information. Lastly, the Chinese central government had been inserting itself in various market interventions and in some cases throwing curve balls.
I don't think anyone would claim that the Chinese stock market's movement is completely unrelated to the real economy, but that relationship must be considered in light of point two which plawolf described, and also the three reasons you described in your own post.
That is to say, it is likely that the Chinese stock market does to a degree reflect the state of China's "economic numbers," but we need to consider if not fully appreciate that the accuracy of that reflection or the specificity of that reflection is likely much more distorted compared to in more developed western markets and economies... because of the various reasons listed such as China's less well developed stock market and less experienced govt regulation, but I think the biggest reason is because of the sheer mass of small, inexperienced and relatively uneducated retail investors who don't have the resources and knowledge of developed institutions.