I'm just going to reiterate a couple of opinions of mine that I've shared in past threads.
A: England need Cook to continue playing at the top of the order for as long as possible, he is nigh on invaluable to the team as a batsman let alone as simply having the most country's capped player of all time as a voice on the field and in the dressing room. With this in mind Cook and the ECB need to decide what keeps him playing at the top level the longest, does he need the top job to feed his ego a little bit and keep him hungry or does it weigh him down and will it ultimately shorten his career. Only Cook will know this and whether he feels he will be able to play by the new skippers rules after being in charge for so long. That is the crux of the matter in my opinion, what keeps Cook in the team for as long as possible (barring a horrendous drop in form obviously)?
B: As much as I'm not 100% sold on Root being the new captain, as others have said I don't think there are many other obvious outstanding candidates. The only other guaranteed starters are Stokes, Bairstow, Broad, Jimmy and maybe Mo and Woakes, no one else has a nailed down spot. Stokes and YJB would have too high a workload if the captaincy was added (I am of the opinion like others that Stokes will make an excellent VC though), Jimmy is at the wrong end of his career leaving basically Stuart Broad as the only other candidate I would think worth considering although, apart from T20, he doesn't really have much captaincy experience.
Ramble, ramble, ramble. Hope that was reasonably coherent