I think everyone chose the automorphism of the square as their example. If so, in your repeat submission, you should provide for inclusion in the last section of the Notes an explanation of why there are 8 equivalence classes of constant terms, and why your axioms are complete for equations between constant terms. Also, try to give a complete description of the terms in the equivalence class of a single variable, and observe that the term model is not the same as the automorphism model (because it must be infinite).
Then, provide your own discussion of the phenomenon illustrated in Quiz problem 3. Work out a similar example showing that the equation (F^2 o x) = x cannot be proved just from (associativity) and the equations between constants.
Write your submission with the aim that it will help students who haven't heard a lecture understand what's going on. Aim for an exposition that could actually be incorporated into the Notes for students to read in future terms, which, with your permission, it will be if you do a good job.