Not a teacher.
I think the answer to your first question depends less upon the word expect and more upon whether you accept that passing an exam and failing an exam are the only two options (which, assuming he completes the exam, they probably are).
In regards to your second question, your proposal gets the point across, but it certainly isn't the only way to convey the idea.
"They don't expect him to pass the exam." is structured in a manner more nearly parallel to your previous sentences.
Student or Learner