I think you pose some interesting questions, and most of us have little idea what is the actual situation. However for what it is worth I put my thoughts on what might have happened. I actually think NP is not an easy guy to work with, this is not at the player level, but at the higher end of management. I feel if he does not get his own way, he easily spit his dummy out, as he did with Milan at Lestra. I feel he has done soemthing similar with us, after the pre-season training camp debacle with Bullard and JC, there was some political moves by the Allam's and probable AP, that this is their chance to get rid of Bullard and his very expensive contract. This for whatever reason, maybe NP felt JC was made a bit of a scape goat, and NP was not happy with this. Whether this was the right or not, is open to debate, but I got the feeling this was the start of NP unhappiness with the situation. It was reported that because of cost cutting exercises, mobile phones and company cars etc being withdrawn from staff, which on its own might not have irritated NP, this coupled with the JC situation he started to be unsettled. Lesta come in with an interest, so he sees a chance to express his disapproval to the board about the above situation, and to show you cannot mess with NP, so I am leaving. The rest is history. Now we come to NB, I personally think it is purely down to his own sensible approach to the job. If he takes on the job full time, then if it does not go well, then he will be sacked and lose a lot of his kudos with the Tiger nation, which he has built up over the past years. Staying as Caretaker this gives him an escape route, until such time that he has proved to himself, the fans and the owners, he can do the job, but also to a degree also see whether the Allam's will but their money where their mouth is and support him.
Fez I think you are thinking to much into it. In my view NP felt he was being shown the door at Leicester. We offered him a new challenge which he accepted despite him seemingly not wanting to leave, and thinking that he was only part way through what he had planned. SGE gets sacked and NP is approached to go back to the club that he didn't want to leave. Added to that he is offered a huge salary and transfer budget. Who in their right mind would turn that down? As regards NB, he has no managerial experience. It stands to reason that he would want to see if he is up to the task with his first job being his home town club in the championship before deciding whether he wants the job full time. Most new managers cut their teeth in the lower leagues. I suppose if it didn't work out, both Hull City and NB would rather that the situation was that a full time manager was appointed in place of NB rather than he was sacked for poor results
I can imagine him taking the job just before the January transfer window opens if all goes well up to then.