Current in a galvanic cell
Although voltage can be calculated from the electromotive series, maximum current is harder to predict due to a number of factors, some of which you've mentioned.


Electrolyte conductivity, which varies with components, concentration, temperature, etc. As you state, weak electrolytes are less conductive. Resistance of a composite electrolyte would be the sum of its components.
Cell polarization, which is an effect at the electrode/electrolyte interfaces. The causes are buildup of gas bubbles, concentration gradients that develop in the electrolyte, etc.
Deterioration of the electrodes and/or electrolyte, particularly under high current drain.
Of course, as @MaxW states, a major factor is cell geometry: area of electrodes and separation due to insulators and electrolyte.


For these reasons, though the maximum current can be calculated from the resistances and EMF, in actual use, cells often fall far short of their theoretical potential (no pun intended).

The resistance of a battery is primarily the sum of that of the cells. Since cells are joined with metallic connections, the cell-to-cell resistance is usually negligible (though I've used poorly designed battery holders with high-resistance spring contacts that severely limited the current, and that damaged the plastic holder due to ohmic heating).