Was Hamlet succesful in dealing with his uncertainties and challenges in Hamlet?
This is one of those questions to which you might receive a whole possible range of answers. A lot of it depends on how a director chooses to stage this play and in particular the title character. It is clear that as the play progresses, we see Hamlet tormented at various stages by a number of uncertainties and challenges, in particular establishing the veracity of the ghost and working out his own response to the Ghost's demands for vengeance. However, I personally believe that one section of the text which shows Hamlet to be at peace comes in Act V scene 2 before his duel with Laertes and the final cataclysmic tragedy. Note what he says to Horatio:
Not a whi, we defy augury; there is special providence in the fall of a sparrow. If it be now, 'tis not to come: if it be not to come, it will be now: if it be not now, yet it will come; the readiness is all, since no man has aught of what he leaves. What is't to leave betimes?
Note the way that at this stage Hamlet appears to be resolved to face whatever fate throws at him through the duel. He appears to be content to face his death and to have reached a position in his life where he is ready to die, having learnt the truth that "no man has aught of what he leaves." I personally imagine a Hamlet who has reached a kind of Zen-like calm at this passage. He recognises that what will happen, will happen, and he just has to accept that. We finally see a Hamlet who is now no longer plagued with the uncertainties and challenges that have dogged him throughout the play.