There are very many things in life where the outcome is uncertain. Studying statistics gives you the tools to make sense of the information, validate the information and helps you to make rational decisions based on statistics.
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It is the population which you are studying.
The answer depends on your aptitude and the level at which you are studying them.
At a guess exponentials, series and statistics would have been important in studying micro-organisms.
rationale and aim are basically the same thing rationale: A set of reasons or a logical basis for a course of action or a particular belief. aims; a purpose or intention; a desire outcome
It is a characteristic that is being studied which is different for different members of the population. The characteristic need not be numeric and the population need not be people - for example, you could be studying the colour of cars.