It is possible to do all that you have mentioned, but it requires an investment of time understanding how Bela builds a project. This also depends on how much you want to keep the students away from code that is not relevant to the current lesson.
When I had a DSP class at university, the professor just pointed us to a specific set of lines in the code in the IDE where we were expected to implement the filter (it was an Analog Devices ADSP...something). He defined the array for the input buffer and the output buffer, made the loop. All we had to do was insert the correct difference equation and coefficients (filter) and press the green arrow on the IDE.
Hypothetically we could have screwed stuff up badly by messing with irrelevant parts of the code, but I recall as a student this other code seemed to magical to touch, so I just stuck with the assignment.
It may be enough to just make a C or Cpp file for the students to edit, where from Bela API you pass only the parameters the student needs and basically give them a template C or C++ function to fill with the DSP concept relating to the lesson of interest.