This sounds like a question from a college student without much plant experience. And college courses on control theory don't cover practical applications in industry very well.
A key point to start with is that in most industrial processes where automatic control is used, time delays are very important factors that affect how well a process can be controlled. Say, for example, you have a steam line and you need to keep the steam temperature from getting too high. Water to cool the steam sprays from a nozzle in the steam line, and water is evaporated by the steam to prevent excessive temperature. The line carrying the water to the nozzle includes a valve with an actuator. A temperature sensor placed downstream of the nozzle in the steam line is used to measure steam temp., and a controller is tied to the valve actuator to keep the steam temp. at a set point.
If, for example, the volume of steam increases while its raw temperature doesn't change, it will take more water to keep the temperature from rising too high. The temp. sensor will note the higher temp., and the valve's controller will open and let more water pass through to the nozzle to keep steam temperature at set point.
But there is distance between the valve in the water line, and the temperature sensor. When the valve changes position, it takes a while before the temp. sensor notices the changed temperature.
If the valve's controller uses only proportional control (gain), control will be unsatisfactory. If the gain is too high, the valve will open (or close) too much in response to a higher (or lower) steam temperature. The result will be overshoots in steam temperature. You will alternately have either too much or too little cooling water. If the gain is too low, you won't succeed in ever reaching set point, assuming steam flow and steam temp. remain constant.
Integral control makes it much easier to control a process by maintaining the correct set point over time. The integral action is dynamic; as error (measured variable minus set point) changes, the part of the output signal due to integral action modulates smoothly (in a well-tuned process) to keep the steam at the correct temperature, in the above simple example.
I didn't answer all your questions, but perhaps this simple example works a little as a primer. Processes get much more involved than just this, but often the basics of industrial process control are as apparent as they should be.