1. Is it possible for the collapse of the Austrian Empire during its 1866 war with Prussia?
2. Separately, what would be the long-term consequences of Prussia making no annexations against France during the Franco-Prussian War?
Well, to answer number 1, it seems very, VERY unlikely. After all, in OTL, the only things Austria lost was some prestige and it's influence over the Southern German princedoms of Wurttemburg, Bavaria and Baden. These areas weren't even part of the Austrian Empire, just client states. For the Austrians to collapse, it would take a lot more fighting than OTL. Whilst the Prussians did defeat the Austrians decisively in Koniggratz, I highly doubt they would've been capable of defeating the entire Empire. And in OTL, the war did destabilise Austria, which meant they had to have the Ausgleich as a means of keeping the Magyars, their largest minority happy. Possibly the Italians could've taken more land (Dalmatia, etc.) but it's unlikely that the entire state will collapse, because many of the nationalist movements are in their infancy and they don't have the strength or political experience to run a country. So I don't think it's possible for the Austrian Empire to collapse during the war, but possibly after, if they're defeated worse and they don't go through with the Ausgleich. The Hungarians will likely revolt and but if they get independence we can likely see the Slovaks and Croats opting to remain in Austria to avoid becoming Hungarian subjects again (yes, sometimes nationalist rivalry in Eastern Europe works like that. In this scenario, Bohemia and Moravia (or at least the former) would be German, further screwing the Austrian Empire's economy. Sorry if this is too long, I got carried away a bit

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As for number 2, I don't really see the reason the Prussians would have that war without taking Lorraine and Alsace, unless they lost or a stalemate ensued. But because I get the impression that the Prussians still win like in OTL, I'll go with that. If the French don't get land taken off them, I presume that they have to pay big indemnities and a non-aggression pact, or buy German goods etc. I'm not sure how this will affect French revanchism. I assume it will still exist, but be far less than in OTL, as finance etc. is not tangible to the majority. "They took our land!" is far more tangible to the average Frenchman (or anyone else, for that matter). The French might put less of a focus on colonisation, which was largely done for the sake of re-establishing their prestige amongst the European Great Powers. Without visibly losing anything, I don't think they will have lost as much prestige. We can therefore see them still quite assertive in Europe, making it harder for Germany to continue to isolate France (without Alsace-Lorraine, is Germany still unified in this scenario? I don't see why not). The French will also be financially better off, without spending a ridiculous amount on essentially worthless colonies (see Tuat). I think that with less colonisation, there will be less antagonism with the UK too, so they might get on better than OTL. In all really, France is better off (although massive butterflies for Africa).