Hot ammonia does not work that well as cold ammonia. Altough the speed of AgCl dissolution is much higher at elevated temperature, "capacity" and effectivity of AgCl removal by ammonia is wrecked by all active reagent evaporation when hot. This effect isn´t that pronounced with HCl as it holds significantly more active reagent with temperature (it even have positive azeotrope with higher boiling point than water). But also with HCl, it is true that you will be better off with cold wash than hot. Use ultrasonic cleaner to speed the washing step with ammonia if you like and have means for it. But it can disintegrate well packed precipitates, so there will always be this tradeoff.
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Depends on what your purity goal is. As I do not have that much experience with sulfate solutions, I cannot directly recommend you the procedures. Espetially with rhodium, which I always just recovered and did not bother with it´s refining.
I am sure that addition of chlorides will precipitate silver, as I worked with silver sulfate solutions and AgCl precipitations from these solutions always worked. I am keen to believe that ferrous sulfate would also work for gold removal.
If there is any gold to be found as sulfate - sulfates are much weaker ligands than chlorides, meaning redox potential of gold would be at worse the same, if not higher than in regular chloride media. Meaning the ferrous sulfate should be quite selective for gold (theory). And platinum - this would be tough to expell from rhodium by standard means since these two has very similar redox potentials. Precipitating as ammonium platinate will help to get rid of some, but not all.
I don´t think there is very significant jump in price between 83% Rh and say 90-95 % Rh. Going for 99+% purity Rh can be very hard and hardly justifying the effort put in. I don´t like refining PGMs due to low premiums when selling to regular buyers, compared with say 70-80+% materials. Too much risk, hassle, hazards and recovery issues for little pay. Big guys know how to do it right and they won´t tell you