You are asking several questions here. Firstly, what kind of questions is philosophy of science concerned with? Here are some of the most important:
How does scientific knowledge advance? Is there a distinctive scientific method, and if so how does it work?
Is there a clear difference between what counts as science and what does not?
Is there a clear way to demarcate good science from bad science?
How objective is science? To what extent is scientific knowledge shaped by sociological or ideological considerations?
What is the nature of scientific explanation? Or, what does 'explanation' mean in a scientific context?
What is the relationship between observation, theory and model?
What is the nature of a scientific law?
What is the nature of causation? Do we need this concept, and if so what account can we give of it?
Is some kind of determinism true, and if so, what are the implications?
What is the relationship between different sciences? Is it entirely reductive in nature?
Does science have anything specific to say about what kinds of things exist? Do theoretical entities such as electrons or quarks exist or are they just useful fictions?
Can evolutionary theory entirely displace the concept of teleology?
What do scientific theories such as thermodynamics, relativity and quantum mechanics have to tell us about the nature of time, space and matter?
What does the general theory of evolution tell us about human nature and mankind's place in the universe?
Are there ethical implications of scientific research?
Are there fundamental limits to what scientific investigation is capable of teaching us? Are there truths that science is not capable of reaching?
Secondly, what impact does philosophy of science have on science?
This is harder to answer. Some scientists, including Newton, Einstein and Poincaré were very philosophical in their approach to scientific thinking. Some philosophers of science have been widely read by scientists, such as Karl Popper and Thomas Kuhn. Other scientists, such as Feynman, are dismissive of philosophical considerations.
Thirdly, how has philosophy shaped our society and enriched our knowledge?
This is a huge question, and you would need to study the whole history of philosophy to answer it. As far as science is concerned, we might say that philosophical thinking historically gave birth to the sciences. In the time of the ancient Greeks, all knowledge was considered philosophy. Once philosophers learned how certain problems could be solved empirically, philosophy gave birth to natural science. As late as the 18th century, the terms natural science and natural philosophy were interchangeable. Philosophical thinking also gave birth to psychology, linguistics, formal logic, economics, etc., so in a sense, everything we know ultimately comes from philosophy.