This extension is necessary to allow the plunger of the syringe to press on the valve. A mini lighter will fit inside a 35 mL syringe. If you use a standard size lighter, you will have to use a larger syringe. The students need to know this position so that they can return the plunger to this position after the gas is released, but before they pull the tubing out of the eudiometer. This accounts for the volume change because of the change in position of the plunger.
Students love to light the gas on fire.
It's not a good idea. There should be virtually no oxygen in the eudiometer, so the flame burns at the top. However, it can get to be a pretty big flame, and there is potential for a burn, or worse, air getting mixed in the eudiometer and causing an explosion. Major sources of systematic error in this experiment are reproducing the original plunger level, and trying to read the level of the gas in the eudiometer while the water levels are equal. If you don't mind the mess, one solution is to completely fill the pail with water at the end of the experiment.