Fire is fundamentally different from water. Water is a relatively simple chemical compound consisting of two atoms of hydrogen and one of oxygen. Fire is not a "thing", not one single compound but the phenomenon we observe when oxygen reacts with burnable gasses. The gasses can be all sorts of things, but usually are methane, carbon monoxide hydrogen and other hydrocarbons. We have answered the question, What is fire? elsewhere at science.ca
Yes you can measure the products of combustion from fire by all sorts of techniques. This was done in the 1700s, and was one of the ways that early scientists discovered oxygen. Water can extinguish fire because it does not react with oxygen. The other liquids you mention can react violently with oxygen present in air and hence they burn. To answer your last question, fire is based on the reaction of oxygen with things. You cannot have fire without oxygen (with a few rare notable exceptions such as gunpowder and rocket fuels which have other oxydizers built in). Think of fire as the oxygen reaction. Fire is oxygen in air reacting with whatever is burning. The reaction is basically the hydrocarbon such as petrol or kerosene combining with oxygen in air to form water and carbon dioxide. There are other things formed, but those are the main two.
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