China uses soft power and regulations to hamper foreign products, especially software. This investment will put Apple in good standing with the govt and could result in an easing of restrictions on Apple's other activities.
I think you're wrong about this.
The political good favor and potential for growth against competitors in China is a huge value. Well worth the investment.
Apple could have chosen to throw money at any of a number of Chinese companies, but they chose Didi. I think it serves more than one strategic purpose, and hints at their intentions with project Titan.
You are probably right. However, by increasing their foothold in such big companies, they definitely have more say.