No, not really; but it leads to a potential "political can of worms" of which members of both organizations are well aware and which are probably best avoided here.
No worries, that's how I took it.
No, I don't think so at all, they're just different from the Bujinkan. And historically, it was not that unusual in Japan for someone to receive menkyo kaiden or equivalent level in one or more arts and then found "his own art" based primarily upon it/them.
It doesn't affect the others. It's just that as Soke of the arts comprising the Bujinkan, Hatsumi sensei is the one entrusted by the preceding Soke (Takamatsu) with their maintenance and with the direction they may take into the future.