Is Air A Conductor?

No air is not a conductor but an insulator
the electrons in air molecules are very tightly bound to their respective molecules in the form of covalent bonds. As a result it takes a lot of energy to rip the electrons free so that they can take part in an electric current. IN general the "break down voltage" of air [the potential difference necessary before the electrons are ripped free] is approximately 10,000 Volts per inch of dry air [humid air is a somewhat better conductor due to the presence of water molecules that are polar rather than covalently bonded]. As to what experiments you can do, the only one I can think of is to use a Van de Graph generator to generate a very large potential difference and then use it to measure the distance over which a spark of electric current will jump.