Can water electrolysis detect the water impurities?
[&hellip;] can this method detect the impurities in water [&hellip;]


In principle, yes. The electrolysis can, as an example oxidize iron ions ($\ce{Fe^2+ -&gt; Fe^3+}$) The latter forms a brownish, voluminous oxide hydroxide, $\ce{FeO(OH)·n H2O}$.

The WHO suggests an upper limit of 0,2 mg/l iron in drinking water.

Am I right that your drinking water comes from a well? Did you perform any analyses on the the water quality or consult local authorities concerning possible health risks and their prevention?


  [&hellip;] or is it just some dirty sales tactic [&hellip;]


I can't comment on the dirty part, but salesmen need to sell. We don't know whether the reference sample was actually produced by reverse osmosis or just a sample of distilled water (which you would not want to drink over a longer time).

Even if reverse osmosis can reduce the mineral content in your drinking water, you might want to check whether the additional costs for operation are really worth it.

Again, try to obtain some information from local authorities.