I used Ion Chromatography (IC) to identify all the anions and cations in the solution and then calculated the balance of total anions and total cations.
If they are in solution (no precipitate), eletrical neutrality requires that the sum of negative charges equals the sum of positive ones, and may occur ion exchange of counter ions, so I think it does not make sense to say that this particular compound exist in solution, but instead you have a mixture of cations/anions in solution.
Jorge is correct. Since these are all dissolved ions in solution, it's difficult to know what compounds they were before they were they were dissolved. Unless, say, you have a large excess of one cation and one anion, in which case you can propose that there was a salt of those ions, and even then, it's still sort of guess-work. Or possibly some information regarding the source of the samples (ie - the environment from which it was collected, the type of sample it was extracted from, or some other piece of information) that would allow you to propose the identity of what dissolved to produce the determined mixture of ions in solution.
As it stands, I don't think that we have enough information to be of much assistance.
"What compounds would I obtain after crystallizing such a cation/anion mixture at a particular concentration at a particular temperature?" may be a better question. Because that's how you move from "independent ions" to "compounds".
I think sulfates of Al and Fe will be present in compound sates as these are less soluble in aqueous solution while all other substances you mentioned will be present in ionized states.
Sulphates are mostly soluble except Ba-, Pb- and Sr-sulphate however, few fluorides of these elements may be in the residue due to low solubility of these fluorides. You may have a mix of different fluorides in the residue.