On the question of a different German Emperor, there is always the possibility to remove William II before he can produce offspring. That would require a PoD before 1882, of course, but in that case you would get
Prince Henry as Emperor - and he was a completely different personality than William, a calm and open man whose idea of the ideal monarchy was pretty much British constitutionalism. An Emperor Henry would probably have left the government to Reichstag majorities, and while the German parties were perfectly capable of international aggressiveness and grandstanding themselves, there would be less gaffes to draw international ire against Germany. Especially the relationship to the UK would probably not deteriorate quite as badly as it did IOTL.
Still, it wasn't like Germany was the only aggressive power on the European scene at the time. It is difficult to imagine how a war can be avoided for another 40 or 60 years or so - until every great power has the nuke, basically. And even then that might not be enough - OTL saw the nuke in action, twice, which helped to instill the fear of nuclear escalation. If there is never a war in which the nuke is used, would it have the same effect ITTL? So, would the nuke lead to the same deterrence against war as IOTL, or would "Mutually Assured Destruction" be seen as exaggerated scaremongering by some attention seeking eggheads?
And even if we do get nuclear profileration as a means of avoiding wars between great powers, well, that 40-60 years gap is still there. And can a general war really be avoided for that long? Even in the 10s already you have enough situations to blow over. Serbia is still ruled by the same clique that gave rise to the Black Hand, so Serbian terrorism in Austria-Hungary is likely to continue. Albania is in pure anarchy. Spain is unstable, at least. Something like the Venezuela Crisis could happen again and escalate. And so on and so forth. And maybe most serious of all, if Francis Ferdinand does become Emperor of Austria and King of Hungary, then an A-H civil war is all but ensured. Either he will try to finally rein in the Hungarian nobility, which would cause Hungarian resistance, or he will try to make his children (from a morganatic marriage, hence not members of the House of Habsburg and not entitled to succession) his heirs, or both. And while indeed the Hungarian nobility was a pain in the ass and any actions against them should be recommended on principle, I doubt an international escalation can then be avoided...
Maybe Francis Joseph lives a few years longer on account of not having to worry about the war, but he died at the quite advanced age of 86 as was. So say he dies in 1920 here, reaching the 90, Francis Ferdinand succeeds him, but 1922 tries to enact his reforms, and by 1924 we have the Austrian Civil War so all we got is a delay of ten years...