What functions should we write for the design deadline?
None whatsoever. All you need to turn in for the design deadline is your set of data definitions and the sample exams as written in your language. Recall that in the first lecture on slideshows, we were able to write examples of slideshow talks before we wrote the interpreter. Something akin to a sample talk program is what we're expecting with your design.
Does our exam system need to distinguish different kinds of wrong answers?
No. It will only need to determine if an answer is right or wrong. Don't read too much into the "order of operations" message on the first run of sample exam 1. That's a more complicated feature than I had intended for you to implement.