Can 自分replace 私 completley? how do you use Jibun to refer to other people?

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I don't thing they are interchangeable. "Jibun" refers to the TOPIC of the sentence. That could be "me", "you", or just about anything. 
彼、自分の車を使う。= he uses his own car.
自分の車ですか？ = is that your own car?

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Basically they are exchangeable with each other. Of course, there are some exceptions. Could you give my some situations you are considering so that I can give you more specific answers. 
I don't understand the meaning of the second question. Do you want to know how to say you in japanese? Then, the answer is anata.

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ほんとうーにありがとう、みなーさん！！＾＾

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I guess not, it means my, or myself(oneself,him/her/on -seself.
While watashi is I

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