As far as I knew I set the correct permissions for the staff groups, but that is all part of my questions, what is correct and what is incorrect?
I've scrapped all the permissions and started from scratch and this is where I am now:
My main admin account and newly created staff account cannot see threads/posts from the test accounts in the Moderator Decisions forum, which is obviously bad as they are the ones who are meant to see these threads/posts as well as the thread creators and be able to adjudicate on them.
This is now working, staff cam see all the posts, but all the other problems still remain.
Let me illustrate about the red button problem.
Here is a screenshot of what my Horizon test 3 account sees.
This account has not posted in the mod forum, so cannot see any posts from my other accounts in there. All good so far. But, as you can see, as well as being able to see who replied last to that forum (my main Horizon admin account) which should be hidden, the red button indicator is showing 18 unread posts for the moderator forum. There are, as you can see, 39 posts in total in the forum, but because the Horizon test 3 account has not posted in the mod forum, then no red indicators should show for that account as its not unread. And even more oddly, the red indicator is showing the amount of "unread" threads rather than posts.
You can't read something, if you don't have access to those posts and threads in the first place...
Additionally, and as already said, this test account can see all the posts from the moderator forum the Dashboard in the "Latest Activity" box. They shouldn't.