What is the role of metal or reagents written on arrows in the given chemical reactions?

A catalyst is a substance or material that will change the rate of reaction without it being consumed by the reaction.

(a) Nickel is working as catalyst. Ethene molecules are adsorbed on the surface of the nickel.

(b) Sulphuric acid is working as catalyst

(c) Potassium permanganate is working as oxidising agent that removes one or more electrons from another atom.