Both of these answers are ways of asking if someone becomes friends with their students.
Sometimes it is not appropriate to be friends with a student whilst he/she is still a student, but once they have left the educational establishment it is okay.
Do you befriend your teachers?
befriend
verb
act as or become a friend to (someone), especially when they are in need of help or support.
Befriend is a great word to use to ask if you becoming or made a friend with someone. I like using this word it makes the sentence simple and easy for the other person to understand.
Let us look at a short dialog to simplify:
Do you ever befriend teachers?
No, not at all it is against company policy
OR
yes my students and I become good friends
"Do you befriend your teachers?"（先生と友達になりますか？）
befriend（動詞）➔ 友達として振る舞ったり、友達になること（特に、相手がヘルプを必要としている場合など）
”Befriend"は「友達になる」ことを表す便利な言葉です。文章を簡潔に作成できますし、相手も理解し易いので、私はこの言葉を使うのが好きです。
会話形式で見てみましょう。
"Do you ever befriend teachers?"
（先生と友達になることありますか？）
"No, not at all. It is against company policy."
（いいえ、絶対にありえません。会社のポリシーに反します。）
または、
"Yes, my students and I become good friends."
（はい、私は生徒と良い友達関係になります。）
"Have you ever become friends with a student?"
Become - when something changes or turns into something else. Like a student changes to be a friend.
have you ever - is this something that has happened before.
"Have you ever become friends with a student?"
生徒と友達になったことはありますか？
Become - 何かが別のものに変わること。例えば、生徒が友達に変わるように。
have you ever - 前に起こったことがあるかどうか聞くときに使います。
Whilst this may not be the most correctly written answer; it is definitely fine as spoken English within the UK.
the important word here is 'make.' It means to create. Essentially what we are asking here is if someone creates a friendship with a student/child who they are teaching online.
Well, the line between work and personal life may be a little ill-defined at times. It would be nice to think that every student is, or could be .... a professional friend?
"Do you ever...?" is a great way of asking questions about what someone does or does not do, as a rule, in their life.
仕事とプライベートの境は時に曖昧なことがあります。生徒はみな職業上の友達と考えるのもいいですね。
"Do you ever...?"（～しますか？）は、人が原則としてしていること・していないことを尋ねる時に使うことができます。
Have you ever become friends with any of your students?
"Have you ever" means that in any moment since they have been a teacher. "To become friends" means that over time you build a friendship. I hope that this helps. :)
"Have you ever"は、「先生になってから今までに」という意味です。
"To become friends"は「友達になる」という意味です。
お役に立てば幸いです。
If you want to ask your English teacher if he/she ever becomes friends with his/her students, you can say:
"Do you ever befriend your students?"
"Have you ever become friends with a student?"
英語の先生に「生徒と友達になることはありますか」と質問したいなら、次のように言えます。
"Do you ever befriend your students?"（生徒と友達になることはありますか）
"Have you ever become friends with a student?"（生徒と友達になったことはありますか）
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