Whew, lot to unpack here... it is indeed fascinating to conjecture what might have happened had the diplomats, generals, and certain leaders not been so infernally stupid in August 1914...
But no, Germany never hoped to equal the RN at sea. That ship had sailed (sorry!
) long before... not only would it be a major provocation and less of a blatant excuse for certain English sabre-rattlers, but it would be godawful expensive, far more so than the Reichstag would bear, and frankly beyond the Empire's shipbuilding capacity at the time. Not to mention that it would be essentially confined to the Baltic as the world's largest fleet-in-being... one would be able to stand on, say, Bornholm and not be able to spit without hitting a battlecruiser
Russia would indeed be much more powerful and effective a military power after around 1917, thanks to French loans, and that would've probably thrown the fear of God into everyone - including the UK and Japan. But could they hold together long enough? My guess is that the social issues that started coming to the fore in 1904-06 would continue, with or without a disastrous war, but would just take a few years longer to reach boiling point...
France? Not so sure... a massive draw-down seems unlikely so long as the German Heer remains the strongest force in continental Europe.
What happens in the Far East without all the major powers distracted by a massive war is a real crap shoot... Presumably Japan (which probably would've issued its Twenty-One Demands or something similar regardless of what was happening in Europe) would continue to press its interest in China, which would run afoul of the UK, Russia, essentially all the European powers with interests in China plus the US... all eyes might would be on Manchuria and the surrounding lands rather than the Balkans as the most likely "powder keg"...