As for the Ottomans, the whole Balkan tinderbox situation would not have occurred if they were not so weak as to be totally unable to defend their Balkan territories against ethnic rebels and their European sponsors. It seems that diplomatic chaos in the Balkans, and a corresponding war over the pieces of the Sick Man of Europe, was inevitable from the very moment the Ottoman hold on the region was first successfully challenged in the Greek Rebellion in the 1820s and 30s.

I can speak to this part but not to the others. There's a few things to deal with here, but in regards to WWI it's that while the origins of the conflict lay in the Balkans, there is nothing inherent in an unstable Balkan region that was going to lead to a general European war. Indeed, one of the reasons why the July Crisis seemed to unravel in almost slow motion and why the news of the assassination of Franz Ferdinand seemed to be so trivial was that in the 1910s there had already been two Balkan wars and several Balkan crises.

That general European war could not have happened without the wider alliance structures and in particular what Christopher Clark calls the "Balkan Inception Scenario", that is, the acceptance on the part of Russia and France to go to war over a conflict between Austria and Serbia that would almost certainly trigger the Austro-German alliance.

if they were not so weak as to be totally unable to defend their Balkan territories against ethnic rebels and their European sponsors....from the very moment the Ottoman hold on the region was first successfully challenged in the Greek Rebellion in the 1820s and 30s.

I mean, that's quite a tall order. The "European sponsors" in the Greek War of Independence consisted of Russia, Britain and France against the Ottomans alone. In other words, the two greatest land powers and the greatest sea power in the world at the time. The Ottoman's ability to prevent Greek independence probably sank with the Egyptian fleet at Navarino as the Egyptians under Muhammad Ali were almost certainly the most competent forces within the empire at the time.

In any event that's a bit of a sidebar to the more relevant aspect of your question:

It seems that diplomatic chaos in the Balkans, and a corresponding war over the pieces of the Sick Man of Europe, was inevitable from the very moment the Ottoman hold on the region was first successfully challenged

I mean, sure, in the sense that without independent Balkan states that WWI couldn't have broken out in the way that it did and that the post-independence Balkans was going to be a mess (as indeed it was long after WWI ended).

But I think that's missing two issues:

Firstly, Ottoman involvement in the war at all was entirely contingent, and perhaps more than any of the Great Powers who went to war in 1914 it was a war of choice, and in particular the choice of the pro-German Enver Pasha. Of note is that the Ottomans were the last of the major 1914 belligerents to actually go to war, not doing so until the Turkish-flagged but German-manned Goeben and Breslau (newly inducted in the Turkish navy with Turkish names, Yavuz Sultan Selim and Midili) attacked the Russian Black Sea fleet and ports on 29 October. There was very little preventing them from maintaining neutrality (and they were even offered inducements to do so) or of joining the Entente (which they pursued, though it's not clear to what extent this might have just been a smokescreen for the imminent German alliance or whether they were, genuinely, looking to join whichever side would offer the best deal.)

Secondly is the issue of why "The Eastern Question" hadn't already led to a general European war. "The Eastern Question" effective refers to the question of "After the Ottomans, then what?" It having been assumed since the mid-19th century that the Ottoman's days were numbered.

The primary answer is that while all of the European powers thought the Ottomans were going to fall sooner rather than later, and everyone wanted a piece of the imperial pie, none of the respective sides could decide what to do about it and indeed were willing to go to war to protect the integrity of the Ottoman empire, which was notably demonstrated in the Crimean War in which Britain and France backed the Ottomans against Russia despite having sided against the Ottomans in the Greek wars mentioned earlier. The outbreak of WWI with the particular alliance structures that it had resolved the question: the empire was to be divided entirely between Britain, France and Russia (the Sykes-Picot-Sazonov agreement). But that was not a foregone conclusion until war actually broke out and until the Ottomans joined the Central Powers.

the Sick Man of Europe

There has also been quite a lot of pushback against this notion of a "Sick Man of Europe" in the past several decades of scholarship. The Ottoman Empire of the Young Turks seemed to have been in a process of revitalization, modernization and mechanization. While it was certainly not a state comparable to, say, Germany or Great Britain, there are no indications that the Ottoman Empire was on the verge of collapse before the war broke out, the Ottoman military consistently out-performed the expectations of the opposing sides (perhaps most notably at Gallipoli and Kut, though also fighting the British to a multi-year standstill at Gaza.) They also more or less continued fighting right through to the end of the Turkish war of independence in 1924 1923 [edit: war ended in 23, Republic of Turkey declared in 24, doh!] and came out of the entire ordeal under the strong leadership of Ataturk.

In any event, a bit of a side question, but as a kind of TL;DR I'm not entirely sure how one could blame the Ottomans for this one, even though they were certainly a part of the overall balance of power and political situation in which the war was possible and then broke out.

Source wise:

I would have a read of Christopher Clark's The Sleepwalkers on the outbreak of the war. For the late Ottoman Empire and their involvement in WWI, Eugene Rogan's The Fall of the Ottomans is quite good. IIRC the relevant chapters in Malcolm Yapp's The Making of the Modern Near East 1792-1923 are also quite good in knocking down the "sick man" thesis.