I am uncertain as to the polarity of ε'' as there are two definitions with opposing polarity.
Yes, the negative polarity corresponds to the usual representation of AC quantities by complex numbers.
I copied the expression from Wikipedia without thinking about the convention. Respectively you get
B = +Aε'ω (leading current of a capacitor is represented as postive susceptance)
In any case, after putting in the ε'' term, you should get
positive resistance and conductance, otherwise the cell would act as an energy source.
The frequency dependency of ε'' isn't but a natural consequence of roughly constant conductivity. I wonder if the complex ε representation is of any practical use for conductivity measurement and calculations.
Regarding interdigital conductivity probe, I think the disadvantages are the non-uniform current distribution and high field-strength at electrode edges, also that it's almost impossible to get an accurate geometry factor by calculations, because small variation of electrode distance and even edge shape have a large effect. Long-term stability is probably poor.