Let me take first question and see whether I can answer all other questions
How to decide whether test process improvement required?
First main factor is degree of customer satisfaction. Each organization will have their own way to measure this. Just for understanding purpose, let us assume we measure this in a scale of 1 to 5 (5 being very happy customer). If we have randomly distributed number of customers in all these five levels may be worth looking at what does it take to achieve 3 and more. Many times answer will be look at process, people, technology and tools used to do the required activities. This is where I feel process improvement focus will help because process can be improved only when you look at all the other three factors above.
First thing in process improvement is to set a goal (where do you want to reach) and assess where do we stand as on today. I recommend to use TMMi framework to assess what you have as practice and how it meets stated practice for all maturity levels. This framework will guide you to set goals and improve the process step by step.
In all processes we do know that people play major role. Technology and tools may help in consistency and speed. How to make sure all in the organization irrespective of their previous experience follow standard discipline for doing specific jobs in a test life cycle activities so that we ensure consistency in the output at each stage of conversion of input to output. This is the place where I encourage people to look test methodology HBT coming from STAG.
Yes, an effective test process powered by HBT ( http://www.slideshare.net/stagsoft/an-introduction-to-hypothesis-based-testing ) had shown significant cost reduction from our experience. HBT helps to accelerate process improvement initiative in the organization. http://www.stagsoftware.com/blog/?p=324