If you are not familiar with idioms, I would not try to specifically write a letter using them. If this is an assignment of some sort, you need to look up some common idioms and think of ways to use them in conversation so you can write a letter.
He has an old head on young shoulders.
The expression "tells the poem" is not idiomatic English, which means that it has no accepted meaning. It could mean the main character in a first person narrative. Or it could mean the author, the person who wrote it. Or it could mean the person who is reciting it out loud.
It is not clear if your PhD is in English or you want to write a letter in English. If you want to write a letter in English you should ask this question: How do you write a letter in English asking for PhD supervision.
I imagine you are writing an e-mail, letter or something like that... I guess we can't translate the expression directly. To end e-mails and letters in portuguese, you can write: "Atenciosamente," or "Cumprimentos"
how do you write the name dianne in korean
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He has an old head on young shoulders.
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'libre comme un papillon'. A more idiomatic expression in French is "libre comme l'air".
how to write an expression letter for the study purpose?
You don't. Stay out of it.
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How do you write an expression
Yes.
You write “Dr and Mrs. Smith”
the same : expression
in a business letter you wouldn't use such an expression. You'd start off by saying something like: I regret to inform you...the expression would be something like: "Lamento informarle que... "