Subscripts are the identity of the element (the number of atoms) whereas coefficients are the number of molecules of the element.
If you change the subscript, you change the number of atoms an element has. This changes the entire element since each element in the periodic table have different atomic numbers.
An oxidising agent oxidises something else. Oxidation is loss of electrons (OIL RIG). That means that an oxidising agent takes electrons from that other substance.
