If we stick rigidly to the assumption "any minute is as likely to draw a foul as the next" then we can model this simply as a Poisson process. The results are shown in the figure below.
Reading off the numbers at each time asked, there is a 74% probability of Durant going the distance if he attempts to play all 20 minutes. If he is benched for 5 minutes, this increases to 83%.
As for part c), there is no trade off involved. Durant should never be benched is the goal is to maximise the probability of playing a certain number of minutes.
For what it's worth I don't think that the assumption of fouls being a Poisson process is true, but then the result of the analysis would entirely depend of what other assumptions are being made.