@Bold 1: That was only true for Kushina and Mito, or did you forget that seemingly everyone hated him? Mizuki knew, Iruka too, Kotetsu, Izumo, and Ebisu to name a few more.
@Bold 2: I don't think that it's as little as you think, also anyone with half a brain could put that together, even Ay (The Yondaime Raikage) knew both of his parents seemingly instantly.
I also highly doubt that Naruto would announce it out loud, he isn't as big a moron as people think, after all; he did keep the fact that he was the Kyuubi Jinchuuriki hidden, also about the Mizuki incident.
In short the seniors. The older people knew about him being jinchuriki and thus hated him. Hiruzen had forbidden them to talk about it. The kids hated him because their parents for some unknown reason disliked him. But they( the newer generation) didn't know about him being a jinchuriki , let alone about being related with Minato.
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Even Sakura didn't know till Gara rescue arc. That was the first time Kakashi let it out. Neji couldn't figure out how Naruto could use any chakra after his attack in chunin exams. Sasuke kept wondering how Naruto was that strong when he fought Gara.
How many people knew about the second piece of info that, him being fourth's own son as well, is still debatable. Itachi knew but when he said he came for "Fourth's legacy " not many put two and two together. So I think this info was related at need only basis.
Iruka knew about him being jinchuriki but the third in that panel still didn't mention him being Mianto's son but kept that ambiguous. Itachi knew probably because he was in ANBU at one point but when he mentioned he was after "the fourth's legacy" not many understood what he was talking about- the word was often seen as reference to him being the jinchuriki alone. Oro mentions a rumour about fourth sealing kyuubi in a kid when he first met Naruto.
There were theories, rumours but few people knew the whole deal.
As for Naruto-- yes he did keep his mouth shut. He in fact has been privy to many incidents where some prime info was revealed and he knew better than to yap about it. There is this tiny factor that being a jinchuriki was not a positive info when people saw him as a monster already. About being son of former Hokage is different. But I agree with you. But the third back then wouldn't know it beforehand. He was a little worried about how Naruto would turn out or affect Konohamaru when he was first introduced. Today we can say Naruto was wiser than he was given credit for- or at least had some instincts which keep him on the right track.
And as I said before- a plot device to make people guess. Today you say it was obvious. But back then when someone said that people often argued negatively and had many theories abotu his dad as well as Mianto. When Minato's ID was revealed, Tobi ID theories took over.
