[Xyrize]

I'm having trouble with a calcium calculation
It's about dissolving ammonium oxalate in a calcium solution, following which a calcium oxalate is the precipitation
This part I understand
Afterwards, the calcium oxalate is put into a sulfuric acid solution
This is where it gets murky for me
I don't understand why calcium oxalate would dissolve in a sulfuric acid solution.
CaC2O4 + 2H+ + SO42-     H2C2O4 + CaSO4
I can't understand this step(edited)
5C2O42- + 2MnO4- + 16H+    10CO2 + 2Mn2+ + 8H2O
Is the following step and it's just as confusing.
I can't seem to understand why these reactions happen, specifically why CO2 is formed.

[AWK]

You should determine calcium in your sample by indirect manganometric titration of oxalate from calcium oxalate.
In the first step, you precipitate calcium by ammonium oxalate from your sample (eg calcium Vit.C tablets).
Then you dissolve pure calcium oxalate in diluted sulfuric acid suitable for manganometry.
In the final step, you titrate oxalic acid with potassium permanganate using well-known reaction, which is quantitative. In this reaction carbon dioxide always evolves.
From the last reaction, you can easily calculate the amount of oxalate bonded by calcium, and from the molar equivalence of calcium and oxalate ==> amount of calcium.

[wildfyr]

I think this a practice problem awk, not a real calcium determination.

[Borek]

I don't understand why calcium oxalate would dissolve in a sulfuric acid solution.
CaC2O4 + 2H+ + SO42-     H2C2O4 + CaSO4

You should compare solubility products and Ka values to see if the protonation of oxalate shifts the dissolution far enough to the right, and to see whether concentration of Ca²⁺ gets high enough to guarantee CaSO₄ precipitation.

I can't understand this step(edited)
5C2O42- + 2MnO4- + 16H+    10CO2 + 2Mn2+ + 8H2O
Is the following step and it's just as confusing.
I can't seem to understand why these reactions happen, specifically why CO2 is formed.

That's just the way it is, oxalate gets oxidized by a strong oxidizer (permanganate). Not sure what kind of understanding do you seek here.