Can the philosophical mysteries be solved at all?
In your post, you ask about why we wonder. I believe that it interconnected with being human and the nature of consciousness. It is likely that wondering and the sense of mysteries led to most of the developments in civilisation, not just philosophy and religion, but the emergence of the arts and sciences.
As children we wonder so much, exploring our surroundings and looking up at the stars. I remember being so fascinated by time, and even though I didn't like maths, I was fascinated by Pythagoras's hypotenuse triangle because it seemed like it contained a hidden mystery. I think that a lot of people give up wondering as much once they get to adulthood. Many settle for conventional answers in religion and science, and move onto more tangible goals, but some keep on wondering endlessly, almost as if dreaming.
I am not completely sure why some people wonder more than others. It may be partly about values. The people who are more career oriented, for example, may gravitate more towards external achievements. It may also be that some individuals are less convinced by ideas which they have been taught, so they carry on wondering. It could be that for many people a less thorough exploration satisfies them until, at some point, life circumstances make them question further.
Personally, the reason why I keep wondering is because I feel that most of the explanations I have been told or read don't seem adequate, or fit together. I am sure that many people I know think that the reading and searching for an indefinite period of time is a waste of time, but I don't think that it is. I also see the whole process of wondering as an important aspect of creativity in its own right. If we stopped wondering at all life could become so mundane and hollow. And, as far as your question of the evolutionary value of wondering, I am inclined to think it acts as a general motivational factor in leading people to unique and creative solutions to all kinds of problems.