On addition of the permanganate to the alkane(in this case ethane) no reaction will occur. However, on addition of the permanganate to the alkene (ethene) a diol will form and the solution turn colourless from purple.
With bromine water:
On addition of the bromine water to the alkane in sunlight a substitution reaction occur.
While, on adding the bromine water to the alkene an addition reaction occurs. When bromine water reacts with an alkene it is decolourised, the reddish brown bromine water turns from brown to colourless.This is because alkenes are unsaturated and contain a carbon to carbon double bond.
Ethane and Ethyne or Methane and ethyne
Saturated hydrocarbon does not react with Br2 water whereas Unsaturated reacts. therefore you can distinguish them if there is no reaction then colour of Br2 will be visible and if there is a reaction then colour of Br2 will disappear.