Today I will talk about the previous candle experiment in detail and answer the three questions that we posed.
To answer the first question, we must understand the chemical reaction that is occurring inside the bottle when we burn a candle. When we use a lighter and light the wick of a candle, we are really starting a combustion reaction that uses the oxygen in the container as well as the paraffin wax of the candle. As this reaction proceeds, we consume the wax and oxygen to create heat, light, water, and carbon dioxide. So now we can answer the first question, the candle goes out because there is no more oxygen in the container to sustain the combustion reaction.
The answer to the second question is related to the first question. When we consume the oxygen, we release less carbon dioxide than oxygen consumed which causes a decrease in pressure. We also create water vapor which condenses and doesn't change the pressure. This decrease in pressure causes the water to flood into the water glass to decrease the volume and increase pressure to reach equilibrium. The changing rates of water entering the container have to with the pressure inside the container at different times during the experiment. While the candle is still lit, it generates heat which causes the air inside to increase in volume. The increasing volume of air partially offsets the effect of the consumption of oxygen.
When the candle goes out there is nothing to generate heat and the volume of the air decreases, increasing the rate at which water enters the container. So this is the answer for the third question.
More about this surprisingly complicated experiment can be found at this link: http://people.math.harvard.edu/~knill/pedagogy/waterexperiment/
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