1. Identify the process involved

   Extraction of aluminium from bauxite mainly involves:

   • Purification of bauxite by Bayer’s process
   • Electrolytic reduction of alumina by Hall–Héroult process

2. Check statement A

   In Bayer’s process, bauxite is treated with NaOH to form soluble sodium aluminate: $Al_2O_3 + 2NaOH + 3H_2O \rightarrow 2Na[Al(OH)_4]$ or written as sodium aluminate solution.

   When $CO_2$ is passed through sodium aluminate solution, hydrated alumina precipitates: $2NaAlO_2 + CO_2 + 3H_2O \rightarrow Al_2O_3\cdot xH_2O + Na_2CO_3$

   So, A is true.

3. Check statement B

   In the Hall–Héroult process, pure alumina has a very high melting point (about $2050^\circ C$). To reduce the operating temperature, alumina is dissolved in molten cryolite, $Na_3AlF_6$.

   Thus, cryolite lowers the melting point of the mixture and improves conductivity.

   So, B is true.

4. Check statement C

   During electrolysis, oxide ions are discharged at the carbon anode: $2O^{2-} \rightarrow O_2 + 4e^-$

   The oxygen formed reacts with the carbon anode: $C + O_2 \rightarrow CO_2$

   Hence, $CO_2$ is evolved at the anode (along with some CO in practice).

   So, C is true.

5. Check statement D

   In the Hall–Héroult cell, the steel vessel lined with carbon acts as the cathode.

   Therefore, D is true.

6. Final evaluation

   All four statements are correct:

   • A: True
   • B: True
   • C: True
   • D: True

So, the correct options are A, B, C, D.