The question asks about the processes involved in the extraction of metal from cassiterite ore.

1. Identify the Ore and Metal:

   • The ore is cassiterite.
   • The chemical formula for cassiterite is $SnO_2$ (tin(IV) oxide).
   • The metal to be extracted is tin (Sn).

2. Evaluate Option A: carbon reduction of an oxide ore

   • Cassiterite ($SnO_2$) is an oxide ore of tin.
   • The primary method for extracting tin from its oxide is smelting with a reducing agent, typically carbon (in the form of coke), in a reverberatory furnace.
   • The main chemical reaction is: $SnO_2(s) + 2C(s) \xrightarrow{\Delta} Sn(l) + 2CO(g)$
   • This is a classic example of carbon reduction of an oxide ore. Therefore, statement A is correct.

3. Evaluate Option B: self-reduction of a sulphide ore

   • Self-reduction is a method used for extracting metals from their sulphide ores (e.g., Cu from $Cu_2S$, Pb from $PbS$). It involves partial roasting of the sulphide ore to form an oxide, which then reacts with the remaining sulphide ore to yield the metal.
   • Cassiterite is an oxide ore ($SnO_2$), not a sulphide ore.
   • The reduction is carried out using an external reducing agent (carbon), not by self-reduction.
   • Therefore, statement B is incorrect.

4. Evaluate Option D: removal of iron impurity

   • Cassiterite ore is commonly associated with impurities, with iron-containing minerals being very common. These include wolframite ($(Fe,Mn)WO_4$) and iron pyrites ($FeS_2$).
   • Wolframite, being magnetic, is removed by magnetic separation before smelting.
   • During smelting, any iron oxides present are also reduced by carbon to form iron metal ($Fe_2O_3 + 3C \rightarrow 2Fe + 3CO$). This iron dissolves in the molten tin.
   • The crude tin (called "black tin") is then refined to remove iron. One method is liquation, where the low-melting-point tin (m.p. 232°C) is melted and flows away from the higher-melting-point iron (m.p. 1538°C).
   • Therefore, the removal of iron impurity is a crucial part of the overall extraction process. Statement D is correct.

5. Evaluate Option C: removal of copper impurity

   • Copper impurities, often from copper pyrites ($CuFeS_2$), can also be present in cassiterite ore.
   • Similar to iron, copper will be present in the crude tin after smelting.
   • Refining processes like liquation and polling are used to remove impurities like copper and iron.
   • Therefore, the removal of copper impurity is also involved in the process. Statement C is correct.

Conclusion: The extraction of tin from cassiterite involves carbon reduction of the oxide ore ($SnO_2$) and the removal of common impurities such as iron and copper. Thus, options A, C, and D correctly describe parts of the process.