1. As to succession - the question is whether there will be a struggle for power or a swift transition.
Hess is, IIRC, still nominal "Vice-Führer". But his actions in 1940 suggest that he might not have been able to get a grip on power.
War hero Göring might have been the popular decision both with the Wehrmacht as with the "electorate". The party might have preferred Goebbels.
A compromise might have been deeming the title of Führer and thus the unificatoin of presidency and chancellorship as being tied to Hitler as a historical exception and separating both to please two men...
However, I do not see an automatic "de-nacification" of Germany in the short-run.
I see three possibilities: a) Goring is quick to affirm his legal prerogative as designated successor and he solidifies his rule by capitalizing on his ties with the Army, the economic elites, and his strong popularity b) he's not as good at doing the above, so a moderate amount of internecine struggle ensues, and he's forced to share power with another leader. Indeed Goring keeping the Presidency and Goebbels becoming Chancellor is one of the most likely possibilities, the SS network was not very developed in 1939, so Himmler is not as likely. c) he really bungles it, the succession struggle gets vicious, the army tires of it, and coups the Nazi regime.
2. The war. Two major questions.
a)Would Germany wish to negotiate?
If Goring emerges as undisputed leader, or the army takes over, basically, yes, neither wanted the war with the Western powers nor Barbarossa.
The position is too favourable - no 2nd front with Russia looms. How confident is the OHL at that point as opposed to 1938 when they opposed war?
Not that much more confident, they feared and expected a repetition of the WWI stalemate in the West, if the Western powers give them a decent deal, say the 1914 borders in Poland, they shall grasp it.
And the year 1940 is a 3rd-Reich-wank in OTL. Hard to outperform that. As bad as it sounds; Germany could only do worse without Hitler as long if it continues the war. (Different situation with an assassination after 1940).
True, unless Goring becomes leader, negotations with the Western powers fail, and he takes a fancy to the Manstein plan. That's far from unplausible. Goring would never initiate Barbarossa, and it is possible that he could pursue a Mediterranean strategy to subdue Britain after BoB fails.
Of course, Stalin is still going to attack in 1942-43, but without the second front with UK, reverse Barbarossa has a decent chance of being withstood.
Alternatively, negotiations with Paris and London during the phony war succeed, in such a case either Stalin dares not to attack or the european powers make an anti-Soviet coalition.
b) If Germany negotiates - would France and Britain be ready to do a Polish Munich? There is still Chamberlain. Maybe restoring Czech sovereignty in exchange for reducing the beaten Poland to a satellite with the 1914-borders would do the trick.
Hitler's death removes the leader that betrayed Munich, so Germany gets back some bit of goodwill. Of course, Paris and London want facts, not words, but if the next German leader is not a racist fanatic that wants to turn all of Poland into Lebenstraum playground, a compromise is quite possible and indeed likely. Both Goering and the Heer would be basically satisfied with keeping Austria, Sudetenland, and the 1914 borders in Poland, and making Czechia and Congress Poland satellites. Pretty much all of Europe since the 1920s expected a German-Polish war sooner or later, and this kind of deal if Germany won, so London and Paris would be willing to deal on this basis. They would almost surely ask for restoration of Czech and Polish political independence, but also would almost surely accept Czechia and Poland becoming Finlandized German satellites.
This because the course of late 1930s has showed that old French 1920s strategy of setting Eastern Europe as a ring of philo-French satellites to contain Germany and Russia both is dead and buried, it can't be enforced without a general war in Europe against Germany (or worse a German-Russian alliance of convenience which the Anglo-French cannot hope to defeat) which London doesn't want unless Germany shows totally uncontrollable, it expends too many UK resources that are necessary to prop up the British Empire, and throws Eastern Europe wide open to the opportunistic Soviet expansion, Britain is indeed willing to fight to the death to prevent German control of Western Europe but is also willing to concede Germany a political-economic hegemony in Central and Eastern Europe as long as it is not created by runaway military aggression. Hitler has the strong taint of betrayed Munich hanging on him, but a new leader gets a lesser dirty slate, as long as he's willing to compromise by backpedaling on some of the 1939 naked aggressions, London is willing to resurrect the Chamberlain strategy of appeasing Germany about all of its sensible irredentist claims and giving it a reasonable sphere of influence in Central-Eastern Europe, and using a satisfied Germany to contain the USSR there.