I agree that they're by far the real threat when compared to Soka Gakkai, especially because Shinzo Abe is their "special adviser," it's a disgusting display of power.
Yes, this is extremely suspicious, I agree. However, I don't think that a murder propagated by the organization is convincing evidence that they're in control of the government. As far as I'm concerned, Soka Gakkai is like Japan's Scientology.
Yes. In the event of a violent revolution, it would be vitally important to ensure that the Socialists secure Tokyo and ensure that the Emperor doesn't make any address from his Palace.