Before you insert an airway, you check if the airway is patent. If there is something in the airway (FBAO) then you would try and remove it with a laryngoscope and McGill forceps. (At least thats how I have been taught)

I'm ab a month late, but supplemental oxygen would be delivered at 15L/min thru your typical oxygen tubing connected to the bag-valve assembly, just like you would with the mask rather than the I-Gel. You could ventilate on room air, but you would expect oxygenation to be not very effective.