sodium nitrate NaNO3 (water) plus sulfuric acid H2SO4 will make nitric acid HNO3 and sodium sulfate Na2SO4 (these sulfate salts will precipitate out for the most part if you freeze the solution, but you cannot get rid of all of them in solution, without distilling off the nitric acid and leaving the sulfate salts behind).
2NaNO3 (H2O) + H2SO4 --> Na2SO4 +2HNO3
if you did not make the home made nitric and freeze off the majority of the sulfate salts before adding it to the metal, you could be left with a lot of these sulfate salts in solution. even with freezing off the majority of the sulfate salts you will still have some of them in solution.
many metals are easily dissolved and are soluble in nitric acid, or as nitrates, some metals are not as soluble as sulfates (silver being one that is not that soluble as a sulfate (only slightly soluble), remember solubility is normally a degree, when we say soluble it can be a degree of solubility, and temperature or saturation and other factors can act on the degree of solubility also.
The blue salts you see I suspect are copper sulfate, I also suspect you will have a mixture of sulfate salts in this mix, silver to some degree and lead.
Copper sulfate is soluble in water, now the copper sulfate once it forms a crystal is a bit harder to get dissolved back into solution, and it will normally take more water to get it to dissolve back into solution, heating can help some here.
silver sulfate (if much in volume) not being very soluble would take a large volume of water to get it all into solution, which would create a larger volume of waste to deal with, so if you had much silver as sulfates in the precipitated salts and wished to retrieve them incineration would be the way to drive off the sulfate, before dissolving the silver back into solution, depending on the way you did this you could have the other metals in solution like lead or copper, so you would have to separate these from the silver.
As you Know the gold is also insoluble and will not be attacked so you will have your gold mixed in with these other salts.
This is one reason if dealing with silver we suggest distilling the home made nitric acid to leave the sulfates behind to get a more pure nitric to work with.