According to the question, a battery was used to light the steel wool by bringing the terminals very close together. When the battery came into contact with the steel wool, current was sent out through the thin wire. This caused the iron to heat up quite well.
Iron reacts with oxygen under these conditions as follows;
2Fe(s) + 3O2(g) --------> 2FeO3(s)
This is the chemical reaction that occurs when the steel wool is set on fire.
When a gas bubbles through water, small droplets of water are usually picked up along for the ride and are mixed in with the gas above the water inside the eudiometer tube. The water vapor takes up room, but isn't the important gas that you need to measure. The table of water vapor is needed to subtract the unwanted water vapor from the collection of gases.
