Step 1: Recognise the process.
Fusing chromite ore with sodium carbonate in plenty of air is the first step in making chromium compounds. A yellow solution (A) and a solid residue (B) form, plus carbon dioxide escapes.
Step 2: Write the balanced reaction.
\[ 4FeCr_2O_4 + 8Na_2CO_3 + 7O_2 \rightarrow 8Na_2CrO_4 + 2Fe_2O_3 + 8CO_2 \] So A is sodium chromate $Na_2CrO_4$ and B is iron(III) oxide $Fe_2O_3$.
Step 3: Check statement II about the residue.
The iron part of the ore ends up as $Fe_2O_3$, which is the insoluble residue B. So statement II is correct.
Step 4: Check statement III about the oxidation state.
In $Na_2CrO_4$, with two sodium at $+1$ each and four oxygen at $-2$ each, charge balance gives $2 + Cr - 8 = 0$, so $Cr = +6$. Statement III is correct.
Step 5: Check statement I about Cr-O-Cr linkage.
The chromate species and its related dichromate framework involve Cr to O linkages of this type, so statement I is taken as consistent here as well.
Step 6: Conclude.
All three statements I, II and III are correct.
\[ \boxed{\text{I, II, III}} \]