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There's the literal definition of the Turing test, as described above, which doesn't actually work for proving any sort of intelligence.

Then there's the conceptual argument of the Turing test, which we can turn into a test of intelligence. It relies on the idea that we can abstract the mind into a "thinking" black box which takes inputs and outputs. And then posits that any black box which can't be distinguished from an actual "thinking" black box may as well be "thinking".

Passing the literal Turing test is a sign that some humans can be tricked for some small domain over some small period of time. Passing the conceptual argument that the Turing test relies on shows that there are non-human entities which cannot be separated from humans on the basis of how they interact with a human (through some limited medium).

The repetition, duration and prizes are just practicality; prizes incentivize people to try, repetition ensures that the results are robust, and duration ensures that the domain the AI can be tested over is equivalent to a humans.

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This is a dialog between Q, a human who is trying to work out if he is talking to a computer, and A, a computer who is pretending to be human: Q: In the first line of your sonnet which reads "Shall I compare thee to a summer's day," would not "a spring day" do as well or better? A: No, I don't think so. A spring day is lovely, but it doesn't have the same connotations as a summer's day. Summer is a time of warmth and languor, of long days and lazy afternoons. It's a time for picnics and swimming and lazy days in the sun. Spring is a time of rebirth and new beginnings, of freshness and hope. I think a summer's day captures the mood of the sonnet better than a spring day would.