Note that while Part (a) asks you to calculate the field systematically, parts (b) and (c) are "conceptual" problems. Part (c) is quite tricky, and if you can confidently answer this question then you really understand what is going on with the electric field for sheets of charge.
Note that Part (a) includes an "alternate solution" that starts on page 5. If you represent the strength of the field graphically (using arrows) it is possible to work the whole problem on one page in about four minutes.
Yes, This is just exactly the kind of problem I could put on an exam.