The general outline for the scenario I had in my head was that Russia would still support Serbia, through diplomacy, sanctions and sale of war material. Basically, the war turns into a proxy conflict. I had assumed that in such a scenario, Serbia would have been forced to fight and could not back down. The Austrian ultimatum demanded the suppression of "all publications which 'incite hatred and contempt of the Austro-Hungarian Monarchy' and are 'directed against its territorial integrity'" and that Serbia dissolve and suppress Serbian nationalist organisations; they basically demanded of the Serbian state that their state apparatuses were to be used to stamp out Serbian nationalism. No early 20th century balkan state would have accepted, except through force, that they themselves had to stifle and stamp out nationalistic sentiment in their own population. I have a feeling that on those grounds alone, accepting the Austrian ultimatum would have resulted in revolution in Serbia.
Two things, they agreed to all demands including the ones you mentioned OTL, the only one they rejected was the one regarding A-H participation in the investigation and prosecution of the ringleaders in Serbia. Therefore, pointing to the others as the ones unlikely for them to accept is weird. You get that is weird, right?
I mean, you could point towards the document being deliberately fashioned in such a manner to seem to be as conciliatory as possible and not truly showcases their real intentions, but it doesn't look like that is your line of reasoning. And I would disagree with the notion of it being such big of a problem. The Balkan states always talked big, but the moment the Great Powers came knocking for payments or demands, they always backed down. From the concessions, Serbia and Greece made because of their financial situations to them giving up any red line they drew in the sand. How long did Greece not accept Crete? What did Serbia do against the Bosnian annexation when they loudly swore to fight to the death? States are normally not completely dislodged from reality.
Furthermore, as stated we know they according to their own statements that they would have accepted all demands if Russa hadn't signaled support to them. Additionally, I have to repeat myself Serbia was not suicidal. Without Russian support, and I mean boots on the ground, they would never engage A-H. Multiple times this threat was raised and each time Serbia backed down, because they knew they stood no chance. Fehervari is right on it, A-H needs to be the aggressor without any ultimatum or any way for Serbia to back down for things to turn to war. Else Serbia wouldn't go for it. They often talked a big game, but these propagandist statements were never meant to be taken to the extreme.
Another point that may change things, it is a PoD before the July crisis. There was a power struggle in Serbia between Pasic and Apis, which culminated near the end of May 1914, you simply have Pasic lose it. The new foreign minister would be Jovan Jovanović, the Serbian minister in Vienna, who was a classical ultra nationalist. With them in charge, you may get such a suicidal response you want.
But also that the Serb Government had given the order to kill AD-FF. (OTL AH investigators found little/nothing).
Gun from Serbian military stock, explosives from Serbian military arsenal and the assassins pointing towards the aide of the second most powerful man in the state. I wouldn't call it little or nothing.
Reconstructing the links with Serbia was more difficult. The weapons themselves were of Serbian make; the revolvers were manufactured under Serbian licence and the recovered bombs hailed from the Serbian state armoury at Kragujevac. On 29 June, Čabrinović named Ciganović as the man who had supplied the team with their guns and bombs in Belgrade. But Ciganović was a lowly figure in the network and in any case a Bosnian exile. Implicating him did not in itself point in the direction of official Serbian complicity. If Ciganović was, as the Italian historian Albertini concluded, working as Nikola Pašić’s agent and informant within the Black Hand, this role was informal and would have eluded even the most thorough investigation. The situation was different for Major Voja Tankosić, a Serbian national who was prominent in the partisan movement, and a personal aide to Apis, the chief of Serbian Military Intelligence. His name was volunteered by Ilić, who stated that Tankosić had not only provided the assassins with weapons, but had also trained them in marksmanship in Belgrade and issued the instruction that they should kill themselves rather than be taken alive. The Belgrade boys initially denied any knowledge of Tankosić; only after they were confronted one by one with Ilić (one of the very few occasions in which prisoner confrontations were used to elicit confessions) did Princip, Čabrinović and Grabež concede that Tankosić had been involved in the preparation of the plot. -Sleepwalkers P.III Chp.7
What is true is that the Austrians handled the investigation badly. Allowing Princip and Grabez to communicate in prison, giving them time to coordinate their stories...there is so much they could have done better, but I don't think a better investigation would have helped. The international situation was so that the other countries simply didn't care. The war wasn't about the assassination of the heir, but a typical conflict between Great Powers.
Because there was nothing; "Apis" didn't tell the government what he was doing.
Like seriously, this is too pedantic to stand on the point of Apis not telling equals them being unaware is ridiculous. Starting with Albertini's great work on the Origins of the War, which goes into length into the statement of a cabinet member of Pasic, which was Ljuba Jovanović the minister of education in the Pašić government, about Pasic what knew. That the man told them that he knew about people who were preparing to go to Sarajevo to kill Franz Ferdinand. Albertini goes even further and names the agent from which Pasic got the knowledge, namely Ciganovic.
The evidence for Pašić’s knowledge before the fact is discussed in Albertini, Origins, vol. 2, pp. 90–97 – Albertini focuses on the testimony from L. Jovanović, reinforced by the supposition that Ciganović was Pašić’s agent; Albertini’s collaborator Luciano Magrini added two further testimonies from Pašić associates, recorded during the war, see id., Il dramma di Seraievo. Origini i responsabilità della guerra europea (Milan, 1929), pp. 106–8, 114–16. The information available at the time is judiciously appraised in Sidney Bradshaw Fay, The Origins of the First World War (2 vols., New York, 1929), vol. 2, pp. 140–46; Hans Uebersberger, Österreich zwischen Russland und Serbien. Zur südslawischen Frage und der Entstehung des Ersten Weltkrieges (Cologne, Graz, 1958), pp. 264–5 supplements this evidence with a scribbled note in Pašić’s hand referring to ‘schoolboys’, ‘bombs’ and ‘revolvers’ found among the papers of the Serbian Foreign Ministry. Vladimir Dedijer’s extremely detailed account of the background to the plot, Road to Sarajevo, concedes that Pašić probably knew in advance of the plot, but proposes that he did so only because he was able to intuit its existence from the incomplete information he had to hand. The more recent accounts, including Friedrich Würthle’s very detailed Die Spur führt nach Belgrad (Vienna, 1975), offer a range of interpretations, but add no new evidence to this corpus. - Footnote 151 Sleepwalkers
The evidence for Ciganović’s role as informant is indirect but strong, see Bogičević, Procès de Salonique, pp. 32, 131–2; Fay, Origins, vol. 2, pp. 146–8; and Albertini, Origins, vol. 2, p. 98. Pašić’s nephew was also a member of Ujedinjenje ili smrt! - Footnote 152 Sleepwalkers
Additionally, we have statements from French and Italian sources, as well as Serbian officials that a warning regarding this incident was given to Vienna originating from Pasic.
Apis did not tell the government, but the government most definitely knew about it.