Starting from "nominal temperatures and rate of heat transfer" means at time of 0, the fluids inside the volume will have the pressure, temperature, etc. at the nominal condition. This will change the initial values of the states, as well as the initial heat transfer. The fluid volumes on two sides of the heat exchanger means that there is some thermal inertia from the working fluids, and if the nominal conditions includes a temperature difference (it probably does!), you'll have some heat transfer and temperature change starting t=0. This is probably why you see that overshoot in MA temperature when TL flow is zero, in your 3rd question.
The error of "Moist air outlet temperature at nominal operating condition must be less than or equal to Thermal liquid temperature at nominal operating condition." has to do with the consistency of the nominal conditions you have set. As the MA flow is heated up in the heat exchanger, its temperature cannot be raised to a value higher than the temperature of the liquid, as otherwise it'll violate the 2nd law of thermodynamics. Roughly speaking Q=cp*mdot*dT, so if your heat flow (Q) is too large, or mdot is too small, dT will become too large, and the outlet temperature will be higher than what's possible (liquid temp.). The Simscape block will evaluate this relationship using the nominal conditions you provided and give you this error if it sees such violation. It's basically telling you that the conditions you provided are physically impossible. Check your data, or math. Usually it's too much nominal power or too little mass flow.
