Which process occurs at the cathode during the process of electrolysis?

$A$ shiny brown coloured element $X$ on heating in air becomes black in colour. Name the element $X$ and the black coloured compound formed.

Which of the following statements about the given reaction are correct?
$3 Fe (s) + 4 H_2 O (g) \longrightarrow Fe_3 O_4 (s) + 4 H_2 (g)$
$(i)$ Iron metal is getting oxidised
$(ii)$ Water is getting reduced
$(iii)$ Water is acting as reducing agent
$(iv)$ Water is acting as oxidising agent

The following reaction takes place when aluminium powder is heated with $MnO_2$:
$3MnO_2(s) + 4Al(s) \rightarrow 3Mn(l) + 2Al_2O_3(l) + \text{Heat}$
$(a)$ Is aluminium getting reduced?
$(b)$ Is $MnO_2$ getting oxidised?

$A$ dilute ferrous sulphate solution was gradually added to the beaker containing acidified permanganate solution. The light purple colour of the solution fades and finally disappears. Which of the following is the correct explanation for the observation?

State one industrial application of the reduction process.