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.
![Probability of Durant making 2 more fouls][1]

The vertical axis shows the probability that Durant has not been fouled out after playing the number of minutes shown on the horizontal axis.

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, he will only be able to play for a maximum of 15 minutes and the probability he will not foul out in that time increases to 83%.

As for part c), there is no trade off involved. Durant should never be benched if the goal is to maximise the number of minutes played.

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.


  [1]: https://i.sstatic.net/Dm9Rk.png