You said, "My Son, I live for you".
I want to know if it is absolutely necessary that the speaker is the son. And how do you change the sentence to indirect speech.
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The speaker could be anyone. If Joe, Pete and Pete's son, Harry are in a room
Pete: My son, I live for you.
Joe (to Pete): You said, "My son, I live for you".
Harry (to Pete): I agree. You said, "My son, I live for you".
Pete: I know what I said! I said, "My son, I live for you." You don't need to repeat everything I say, already!
If Joe was reporting this he might say:
Pete told his son that he lived/lives for him.
(This has pronoun ambiguity)
And Harry might report
Dad told me that he lived/lives for me. What a weird thing to say!
And Pete might report
I told Harry that I lived/live for him. I hoped to have a moment, but him and Pete ruined it by just repeating me like strange robots. What's up with that?
Backshifting is, as usual, optional.
Yes - anyone can quote anyone verbatim. When they do, they normally make it absolutely clear that they are doing so. There are a number of ways they may do this verbally; in writing, the quotation marks serve the purpose. I can find no fault with your example.
It is probably more common for someone to state the meaning of what someone said than to quote them verbatim, for example:
Father: My son, I live for you.
Son: You said that you live for me.