Some useful reference may be from:
How to experimentally construct an imaginary(complex) potential.
what's its physical meaning and what does it represent?
In the case of:
a. purely imaginary potential
b. both real and complex part are not equal to $0$.
Also a further question 3: Observables were represented by hermitian operators and with real eigenstates. However, this meant whenever we "measure" the potential, it must be real. Thus we could represent all potential at any given place in terms of real eigenvalues. Then does it mean that all imaginary potential could be converted into real potential? And was imaginary potential legit at all?