Did Kakashi killed his best friend?

no he didnt, his friend was killed by a ninja (this is manga im talking about) and his friend gave him his sharingan eye (one eye was covered by the giant boulder that crushed half his body) for a birthday present.

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not birthday present but a gift for Kakashi becoming a Chunin and although Kakashi have mangekyo sharingan which you can only get if you kill someone close to you like a best friend or brother. it still unkown how Kakashi can use mangekyo sharingan.