check the Manga when Iruka asked Kakashi not to nominate Naruto for Chuunin he said to Iruka "he was Six Years when he became Chuunin".
Yes. Iruka stated that back in part one when he was discussing whether or not Team 7 should participate in them.
That has nothing to do with Kakashi being a Jounin at age 12. Nothing with Kakashi's advancements was shown to be a mistake.
You said he was shown to be 12 and a Chuunin. The only time we see 12 year old Kakashi is in the Kakashi Gaiden arc that was shown upon the conclusion of part one. He was already a Chuunin (since age 6) and promoted to a Jounin on his 12th birthday. There's nothing wrong with this.