Hitler does have a designated successor, Goering, who is an incompetent jackass, but at least regular military. Most time lines have Himmler winning out, but I don't know. IIRC the Waffen SS isn't a big force yet (not that they ever were big enough to take on the Wermacht in a straight fight), and the SS/Gestapo don't have anywhere near the level of domestic control that people usually think. Goering might be able to take charge. If he does, major purge. Bormann, Himmler, and a lot of high-level SS officers will have to go.
If the Soviet command decides to take advantage of the situation and attack (abandoning their careful planning to spring the trap on Zitadelle), it won't be nearly as successful as Kursk was OTL. German officers famously are pretty good at defense when left to their own devices. Of course their chain of command will be a mess, so who knows? I think Zitadelle/Kursk might happen at about the same time (it'll take Goering a couple of months to get organized if he can at all), and with about the same result.
The Axis will probably bug out of Africa (this is after Kasserine Pass).