誰が田中さんのカメラを壊したの？って英語でなんて言うの？

In may not be so easy to identify the culprit who actually broke Mr Tanaka's camera! The person who did it may be too shy or too embarrassed to own up to this misdeed.
To own up = admit to having done something wrong or embarrassing, confess (to), admit to, admit guilt, plead guilty, accept blame/responsibility, acknowledge (that), tell the truth (about), make a clean breast of it, tell all
"He never owns up to his mistakes."

Who has broken Mr. Tanaka's camera? A polite way of asking a class who has broken the
camera. Although it would be difficult for someone to answer this question in front of other
class mates.

Mr. Tanaka's camera is broken, can someone please tell me who did it?

There are many ways to ask this question. Here are a few additional ways you could ask about the broken camera.

If you are the one trying to find out who broke the camera, you could ask,
"Did anyone see who broke the camera?"
"I am looking for who broke the camera, did you see anyone using it?"
"We need to find out who broke the camera, does anyone know anything?"
Maybe no one knows, but you might recieve clues as to who broke the camera.

Explanation:
'Who' is used in this case to ask which person broke the camera. In this case 'who' is the subject.
Starting a sentence with 'I'd like to know' informs the listener that you would like to find out more about something.
You can use 'could someone tell me...' if you are questioning a group of people. If you are questioning a single person then you can use 'can you tell me...'

If something is broken then you might want to find out who broke it a simple way to ask is 'who broke Mr Tanaka's camera?' if you think someone knows who has done it but hasn't said anything then you could ask 'can someone tell me who broke Mr Tanaka's camera?'

Unfortunately using the sentence "Who did break Mr.Tanaka's camera" doesn't make sense, in order for it to make sense we would have to re-arrange the sentence to "who broke Mr tanaka's camera?" due to 'did' often refers to a past tense and 'break' often implies present and future tense.
"Whom was the culprit of damaging Mr.Tanaka's camera" is a very formal and polite way of asking who was responsible.
'Whom" is a very formal and polite way of asking 'who'
'Culprit' is another very formal way of saying who was to blame/responsible.