*solved - can't I use 'unearth' there. It doesn't seem natural to me too, but could you tell me why. (Unearth means to discover. I was thinking that mysteries are either solved or unsolved but I guess you could discover a new mystry too so use whichever you wish

)
* man is a restless - If I was thinking about his 'becoming' something he was not before, would this apply? (I guess I have thought that man has always been restless

but as it is your text please write it the way you see it.)
* man grows constantly in knowledge - What if I'm thinking of the "greatness/degree" of what he's learned? I used "intensely" in my original writing, doesn't it fit the sentence well? (We usually refer to greatness/degree of knowledge as "depth" thus: He has great depth of knowledge.... so you might want to use the word depth to describe amount

)
* continue to be elude him - I think you mean " continue to elude him", right? I like this very much, thanks! (Yes you are correct. I was going too fast I guess

)
*However hard works - I thought you missed the "he" here. (Yes

)
* He has crossed every sea, and traced every valley. - This one riddles me. All the preceding sentences, you've changed to the present tense while this one remains as is. Do I need to convert it to the present? (I thought this might confuse you. I used past tense here because it describes things that have been accomplished where as the other things are still ongoing)
* There is no greater joy for man then to accomplish the purpose for which he was truly created. - And this one I like the most. You gave me a wonderful conclusion. Thanks a lot Carl!
You are most welcome. I am happy to help. You have a flair for writing and you have great insight into the human condition.