Is Isothermal Process Always Reversible?

Isothermal expansion can surely be irreversible if you make it so. In fact, any process is usually at least a bit irreversible, and truly 100% reversible processes are impossible.

Is isothermal process reversible or irreversible?

Both isothermal and adiabatic processes sketched on a pV graph (discussed in The First Law of Thermodynamics) are reversible in principle because the system is always at an equilibrium state at any point of the processes and can go forward or backward along the given curves.

Is isothermal process necessarily internal reversible?

But the isolated statement "isothermal heat transfer processes are internally reversible" is false: they can be reversible or irreversible.