When did most Chinese have to use the public phones to contact each other, as what you can see in the black-and-white picture?

Not too long ago. The picture was taken in 1988 at a fixed-line service with by roadside vendors in Beijing.

About 10 years ago having a telephone line connected to one's home was a privilege comparable to driving a Mercedes Benz. At the time there were only a few such cases in a large neighborhood in Beijing.

(China Daily October 23, 3008)