Alliance with France? No way. As France in general and especially the Bonapartes are a "persona non grata" in the foreign affairs of the german states. Whoever allies with France would lose the support of the german minors. Prussia tried this (economic arrangement / trade deal) to 'blackmail' the Zollverein and got away with it but lost all its support among the german minors.
Alliance with Russia? Possible, as long as both states continue their restrictive/reactionary politics the "Holy Alliance" might hold. But sooner or later (most likely sooner) the Balkans, straits and pan-slavic sentiments will brake this alliance. Especially after the Crimean War an alliance will be highly unlikely.
An Alliance with Russia to beat Prussia? No way. The Prussians had way better relations with the Tsar since the Convention of Tauroggen as the Austrians ever had. You really would need some major butterflies.
Prussia weaker than Austria before 1862? Unlikely but close. Before Bismarck to reform the military against the parliament's will (-> Heereskonflikt) Prussia had seen a decline of its military capabilities. Since the early 1850s officers and politicians were convinced that a major reform was needed. This decline let the prussian king and generalstaff back down from a participation in the crimean war in 1853. Right at the moment I'm not sure which side the Prussians favored. But both Russian and France forces seem to me more numerous than Austria's army. So between 1850 and 1862 I think it would be very close in numbers, but the Prussians had an advantage in mobility and logistics as they had way more railroads allready in this timespan.
A democratic Revolution leading to a "Federation of the Danube"? Highly unlikely. The Revolution of 1848 was not a united movement but on the contrary its forces where very distinct from each other. In the german parts of Austria it mainly was driven by the desire for a reformation of the state and goverment, at least they wanted a constitution at best they hoped for voting rights and a (strong) parliament. The other ethnicities in the empire wanted their own (nation)state and hence pushed for the dissolution of the Austrian Empire. Nationalism and nation-building were more important than constitution and other reforms as it was the common denominator of those otherwisely highly diversified movements. This is especially true for the italian, bohemian and hungarian parts of the empire. With this in mind, how should they form a "federation"? Closest to this comes the partition into three parts: austrian, hungarian and croatian which was supposed by Archduke Franz Ferdinand IOTL if I'm not mistaken.
Granting more autonomy will lead to a more powerful Austria? I doubt that, but this might be just me. IOTL the hungarian parliament blocked almost each and every budget and reform of the military and doesn't pass budgets without demanding more rights for the hungarian parliament or the like. And with regards to the etnic sentiments (eg. the croatians hated the hungarians as they were treated by them as second rate citizens) this would only lead to a more self-blockading system of government.
Extending the german population by annexing the south german minors? Doable but might not be sufficient. By south german minors Baden, Bavaria, Württemberg and one of the Hessian states (I always mix them up) are meant. This is the line on which both austrian and prussian diplomats agreed (though never at the same time) in case that the "Deutsche Bund" is dissoluted and Germany partitioned between the two Great Powers. Those states are not very populous nor are they industrialized at that point in history. This helps a bit but not enough as even bolstered by the population of the annexed south german states the germans wouldn't even hit the 50% mark.
Extending the german population by annexing additional german states? Even as this might not be violiting the "no Großdeutschland" rule it can only be done by a major war against Prussia. And maybe France too, if they couldn't be paid off.
No Großdeutschland? This is not only tough but in my eyes impossible. Either you let Austria beat the Prussians in the struggle for Germany and thus "Großdeutschland" is formed by Austria in one way or the other. Or Austria gets beaten in this struggle by Prussia and therefore would not become a superpower (and especially not the one and only continental superpower which seems to be the maingoal). One could argue that it draws its power from other regions, lets say by dominating and annexing the balkans or the italian states. But why hasn't happened it IOTL? Because even by letting its ambitions in Germany go (early) it would not have the necessary power to fend off neither the Russians (in the Balkans) nor the French (in Italy) which both would bring in Prussia if Austria has any ambitions in Germany left. If German Unification is not gonna happen than Napoleon III. will become gready sooner or later and swallow the minors, making France once again the continental superpower.
That the scattered regionalism would come to an end seemed like a no-brainer for most german politicians and diplomats after 1848/49 (for the time between 1815 and 1848 I can't tell for sure). The minors were going to be a) united and dominated by Austria (Prussia as a part of the empire) b) united and dominated by Austria (Prussia remains independent) c) united and dominated by Prussia (leaving Austria out) d) united and dominated by Prussia (including the german parts of Austria) e) united in a confederation and "ruled" by a council of five, including Austria, Prussia, Bavaria, Saxony and Hannover iirc (This is known as "Trias-Lösung) f) partitioning of Germany, North dominated by Prussia, South dominated by Austria
As a matter of fact chances weren't too bad for Austria to win the struggle for Germany. The austrian plans were more pleasing to the minor german states and even Wilhelm I. at one point was about to give in to the Austrians which only could be prevented by major decisive action of Bismarck himself. And for most of the time between 1850 and 1866 most german states were in favor of Austria as dominating power.