Chetori?= informal way of asking "How are you?" Haleh Shoma Chetor Ast?= formal way of asking "How are you?"
C'est combien? is an informal way of asking how much something is (costs).
what state are you asking about
I assume you meant "petition." A petition is a formal written request typically signed by a group of people, asking an individual, organization, or authority to take a certain action or remediate a specific issue. It is a way for the public to demonstrate support or opposition to a cause.
You just say: "This is a formal event".
Making an appeal means asking for a review or reconsideration of a decision, usually in a formal way, in hopes of changing the outcome.
"How art thou" is an old-fashioned way of asking "How are you?" in Old English. It is a formal or poetic way of inquiring about someone's well-being.
Are you asking if this expression would be acceptable in formal English? It may not be the worst usage in formal English, but I would look for another way to say it. It is idiomatic, and may not give a consistent meaning to any reading expecting standard usage.
I'm not sure whether you are asking about "formal" (which is an adjective) or "in" (which is a preposition).
I think that it's basically the same but "shall" sounds more formal than "may". may you is asking a question 'may you please do that'. but shall you is a more formal way of saying should you?
"Whence come ye?" is an old-fashioned way of asking "Where do you come from?" It is a more formal or literary way of inquiring about someone's origin or source.
"Comment vous appelez-vous?" in French means "What is your name?" It is a formal way of asking someone's name.