The two responses are the same in the TTX experiment because the delayed rectifier K channels do not exhibit the same type of inactivation as seen in Na channels. The rising phase of this action potential is due to an influx of Na and Ca cations. The falling phase is due to a combination of a voltage dependent K current and a Ca-activated K current. This means that the hyperpolarization is caused by a closing of channels. Given our knowledge of the distribution of Na, K, Ca, and Cl ions across the membrane, the IPSP must be due to a decrease in an inward Na or Ca conductance or a decrease in an outward Cl conductance.
Some cells release multiple transmitters, each causing a different response post-synaptically.
In this case both students are correct since the data in the question cannot distinguish between the two possibilities. However they cannot be due to vesicular release since they still occur in the absence of external calcium. Hence this is a case of non-vesicular transmitter release. To test this conclusion I would block vesicle fusion pharmacologically and see if the mini-mepps disappear. My prediction is that they would remain.