Why does the adiabatic exponent decrease at the ionization zones?
There are two things going on. (1) When you add heat to a gas that is on the threshold of ionisation or partially ionised, some of that heat goes into ionisation. This means that it takes a much larger amount of energy to produce a rise in temperature. (2) However, as the gas becomes ionised the number of particles per unit mass also increases and so the pressure increases at a given temperature. The net effect is that $C_V$ (heat capacity for a fixed volume) increases by more than $C_P$ (heat capacity for a fixed pressure) and so the adiabatic index decreases.

It is a tricky and detailed computation to work out how $C_V$ and $C_P$ change as ionisation proceeds. An example calculation for pure hydrogen gas is give on pp 123-126 of "Principles of stellar evolution and nucleosynthesis" (1983, D. Clayton). Both $C_V$ and $C_P$ increase drastically (by factor of 30-40) as ionisation increases, both peaking at around 50% ionisation before falling back to exactly twice their unionised values once the gas is completely ionised (when it just behaves like a monatomic perfect gas but with twice the number of particles per unit mass). However, the behaviour of $C_V$ and $C_P$ are slightly different, $C_P$ increases by less than $C_V$, and so the ratio of $C_P/C_V$ changes and goes through a minimum at around 50% ionisation before regaining the standard monatomic gas value once completely ionised.