Can we make a rusting battery
Sure! A nickel-iron battery uses the oxidation of iron at the negative plate to produce about half the voltage. Though invented by Jungner, it's often called an Edison battery. See http://en.wikipedia.org/wiki/Nickel%E2%80%93iron_battery.

There are very low power semiconductor devices which could be powered by an iron battery. You could make three or four small cells from iron nails and a more electronegative element, e.g. lead, to power a digital watch; even without optimization to remove layers of hydrogen and rust, it should operate for months. 

For some other low power ideas, see https://www.enocean.com/en/energy-harvesting/.