every N in N2O5 has 4 bonds

That's a dangerous approximation, no wonder it produces strange results.

Note that ON are just an accounting device that helps in balancing redox reactions, in general there is no real world physical property that could be measured and called ON.

If a solution contains 0.01 mol/L of Hg²⁺ and 0.01 mol/L of Bi³⁺ what mass of S²⁺ ions will be necessary to precipitate at least 99% of the bismuth present in one liter of this solution? And if the solution had lead instead of mercury, would the sulfate's mass be the same?

KspPbS=3,4x10^-28
KspHgS=2×10^-53
KspBi₂S₃=1,6X10^-72

So, for letter a, I initially calculated which one of the cations would precipitate first(HgS). After that, I considered the following equilibrium:

KspHgS=[Hg²⁺].[S^2-]
As I know the concentration of Hg2+ and the Ksp, I could determine [S^2-].

I don't know what I have to do after that, could someone help me?

Each N  has 4 bonds  and a positive charge, 2 oxygen have a negative charge, what gives mesomer 5 bonds.


https://encrypted-tbn0.gstatic.com/images?q=tbn:ANd9GcSkkeqGM18NZS8fsURSyPtdVxqhmUrtJF2iWXcQsw&s=0

https://encrypted-tbn0.gstatic.com/images?q=tbn:ANd9GcTx_Ean9Hgk0RchTx0r42Gh7a4s4lqRutmU1w9sRA&s=0

Here we have nitrogen pentoxide, the anhydride of nitric acid, no peroxide group.

I agree.  On the other hand, I think that the strategy that the more electronegative atom essentially owns the electrons works well here.

I do not have time for a complete answer, but in compounds such as peroxides, the oxidation number of oxygen is -1, not -2.  I do not think that this exception applies in your case.