Oxygen is consumed during the initial burn that creates the Oxide "Shell". Once the coating is there the chromium is protected from further oxidation so the answer becomes no. Though the amount of oxygen that it consumes will be negligible under normal circumstances.
Most heating elements use Nichrome 80/20 (80% nickel, 20% chromium)
wire, ribbon, or strip. Nichrome 80/20 is an ideal material, because
it has relatively high resistance and forms an adherent layer of
chromium oxide when it is heated for the first time. Material beneath
the wire will not oxidize, preventing the wire from breaking or
So the first time when it creates the oxide coating yes it ill consume oxygen to create the Chromium Oxide. After the initial coating the metal resists oxidation so it should consume little if any oxygen unless the oxide coating is removed.
Oxidation resistance can be attributed to the formation of a highly
adherent protective scale. The adherence and coherence of the scale
can be improved by the addition of small amounts of other reactive
elements such as zirconium, silicon, cerium, calcium or similar. The
scale thus formed is a mixture of nickel and chrome oxides (NiO and
The source above has confirms the Wikipedia site description of the Oxide process
As for the humidity, the chart here shows how relative humidity changes by temperature. The fixed measurement is "absolute humidity" and is measured in grams per cubic meter. As temperature increases the absolute humidity will stay the same but the relative humidity, how it feels, goes down. So the effect is it feels like the air is dryer but there is the same amount of moisture in the air.