1) I think that the best time to hire a DoF, was the day Fergie left. The second best time was the next day, and the third best time was a day later. You get the drill. So the best time for now, would pretty much be tomorrow or so.
2) I really don't buy this identity thing. It is a bunch of nonsense that really does not exist. Just an imagination on describing whatever is happening at that particular successful time. I mean, what really is identity of United, would love to know it?! What is that of Madrid? I guess winning a lot of UCL. But then that is desirable for every club.
I also don't buy this special manager for a club. I believe that SAF would have been great anywhere (given enough power obviously), as would have been Cruyff, Mourinho, Pep, Klopp etc. Yes, Zidane too.
3) Oh but it is. Just go check Moyes' thread in 2013-2014. In every club, the manager is another employee (a very important one obviously) who is there to serve the club. At United, the manager is a demi-god, and the club is there to serve the manager.
About your last point, more or less yes. I don't think he is good and I don't think this season has been great, but at the same time I do not trust Ed to fix this (he has been awful in most football-related things), I think we have left it late, I think this summer is a bad one to change managers (no pre-season), I am not sure if anyone except Allegri is good enough and available, and not having a structure above the manager means that it would most likely be another clusterfeck. So I guess I have to become a theist again.