Supposing the Edwardian world just keeps puttering on...

All points out to what you say. I just don't want to completely discount a possible formation of a German Nazi-like party, thinking that while it would not be an autonomous development, it still might be a contagion.

I agree, it is probable that the German right wing might at some point try to merge to have a chance to counter the majorities of the SPD and Zentrum (prior to 1918, elections worked FPTP, this might continue ITTL). In a continued Kaiserreich, such a party would probably rather look like the DNVP than the NSDAP.
Without the very special circumstances in OTL's Germany, it would be less radical, less "socialist" and lack the degree of political violence (which would not be tolerated by the authorities). The constitutional monarchy, compared to the Weimar Republic, would have a lot more legitimacy. To many voters, a party proposing a radically alternative system, would not be taken into consideration.

Probably the alliances would be more flexible, as they were before WWI. But there would still be large national sympathies: Britain and France due to friendly rivalry, Germany and Austro-Hungary due to the germanic element.

The latter is probably true, unless there comes a strong pan-German current (alt-Nazis) into Berlin's politics.
Franco-British-Alliance might very much ebb and flow with the degree as to how much Germany is perceived as a threat by London. It quickly unraveled after 1919 and was very much an effect of intensive lobbying by Edward VII in person. As a long-standing fixture in 20th century Europe, I give it a 30% chance. As an on-and-off option for both, 70%.

France and Russia might become long-term partners rather due to the heavy economic entanglement underway than by the Anti-German geostrategical possibilities (a Chimerica-situation).
 
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