This is not a normal English grammar structure.
The rules of Jeopardy require that contestants answer the clue in the form of a question.
I tend to think of it this way... it's a backwards game show. Most game shows require that the host ask a question:
Who was the first president of the United States of America?
And contestants provide the answer:
George Washington.
With Jeopardy, it's the other way around. The host is answering the question while the contestants are asking it...
So, if the clue is:
This man was the first president of the United States of America.
The rules require the response be
Who is George Washington?
If they fail to do this, even if they're technically correct, they lose points.
So, if a contestant answered:
George Washington.
They would be wrong by the rules of the game.
As to their hesitant tone, sometimes they're not completely sure of the answer, so they're guessing.
'First and foremost' and 'Last but not least' are phrases that are used in addressing a formal speech or a formal text. They are not wrong. The software that you are using probably check clichés of words with similar meanings, because 'first' and 'foremost' are synonyms, same in other case.
Best Answer
is 100% natural and common.
I've never heard it, and it sounds terrible to me, though I suppose technically the grammar is good.
Without the contraction, it sounds OK, but is not common at all. It sounds overly formal or stuffy.