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.
It's a little unclear to me (native American English speaker) whether in polite sentences the modals are, formally, in the subjunctive mood, or indicative but counterfactual conditionals. (Some reference here: https://en.wikipedia.org/wiki/English_modal_verbs#Past_forms)
Either way, though, they are polite because they express a condition that is doubtful or contrary to fact. You can see this behavior in some other examples:
He can go to the store
Implies simply that he is able
He could go to the store
Implies that he is able, but in most contexts implies that he won't. When you say:
Would you go to the store with me?
You're expressing a doubt as to whether or not they will, which is a less forceful way of asking.
Best Answer
The subject and auxiliary verb are normally switched order in a question. This process is called a subject-auxiliary inversion. That's why the auxliary verb precedes the subject in your first example.
However, when the question is embedded in a sentence(or inside another clause) this process does not occur.