Can anyone explain the reaction mechanisms of these synthesis?
The ammonium chloride, calcium hydroxide, ammonium sulfate, and sodium hydroxide are all ionic compounds, and when dissolved in water they dissociate into $\ce{NH4+}$, $\ce{Cl-}$, $\ce{Ca^2+}$, $\ce{SO4^2-}$, and $\ce{Na+}$ ions. The $\ce{NH4+}$ ammonium ion can donate a proton to the $\ce{OH-}$ ion, creating $\ce{NH3}$ and $\ce{H2O}$. The other ions don't really do anything, so these spectator ions remain in solution but the charges are still balanced. If you removed the ammonia and water, which is easy with a vacuum, you'd be left with the $\ce{CaCl2}$ and $\ce{Na2SO4}$ salts. These reactions will have some equilibrium, with $\ce{H2O}$ donating a proton back to $\ce{NH3}$ to form $\ce{NH4+}$ and $\ce{OH-}$ again.