How do I separate Zinc Sulfate liquid other heavy-metal

I do not have any experience with the DC current method you describe but as the metals you list tend to plate onto a cathode before zinc you should be able to use that method to purify your solution. However, I would caution that this method might be difficult to control to achieve the degree of purification you require.

Below is a method widely practiced in the zinc metals refinery industry to prepare ZnSO4 solution for electrolysis. There are many papers and books that detail the process and the quantities of reagents needed. The basic procedure is:

First stage:

Impure Zinc Sulfate solution is heated to ~ 60 deg. C in a stirred reactor (do not entrain air in the solution). A stiochiometric amount of Zinc dust (< 75 micron) is added to remove Cd, Cu, Tl, some Ni, Co and other elements. The formula (1.0 + 1.2*[Cu] +2.0*[Cd]) = g Zinc Dust / l of solution (concentrations in g/l) should work reasonably well to start. After ~30 min. the slurry is filtered to remove the impurities. Monitor the [Cd] in solution to determine when to filter (< 5 ppm).

Second Stage:

The filtrate is then heated to ~90 deg. C in again in a stirred reactor. Antimony at a ratio of ~0.08 mg Sb / mg Co in the filtrate. Copper Sulfate solution is also added at a rate of ~20 mg Cu / l of solution to speed up the reaction rate. After mixing, Zinc Dust (< 200 micron) is added (0.5 + 100*[Co] + 50*[Ni]) = g Zinc Dust / l of solution (concentrations in g/l), also a starting point. After ~120 min. the slurry is filtered to remove the impurities. Check the [Co] in solution to determine when to filter. Should be < 0.1 mg/l. If [Co] OK the other elements are usually removed also.

Using this method we routinely get Zinc Sulfate solution that assays at: < 0.1 ppm [Co], [Cd], [Cu] and <0.01 ppm [Sb], [Ge], [Tl], [Ni], [As]. The Hg, Se and Mo should also have been removed.