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Q1: All references to supply air refer to the air supplied to the zone, S2 in your diagram. S1 in your diagram is the recirculation air. The steps in your description above are not correct. If I'm following correctly, the confusion comes from calculating the supply air mass flow rate multiple ways during the process, because it may be governed by the outdoor air flow or by one of the temperature limits. It is determined both ways and the greatest is used. Ultimately, there is only one supply air mass flow rate - that is what enters the zone. This is what the engineering reference steps are trying to describe.
Q2: Yes, sort of. There is no coil model in the ideal loads system. The change in enthalpy (broken into sensible and latent portions) between the mixed air and supply air conditions with the supply air mass flow rate are used to calculate heating/cooling loads which are reported and metered as district heating/cooling.