Russia not even need to enter at all, hungary alone can derail any austria effort and i doubt they will annex anything else that Bohemia(the whole thing, specially Prague), as prussia never liked the austrians, we could see an early Ostmark with Moravia that they accepted in the prussian empire at all
So let's consider every factor here.
In order to see Hungary become independent, Austria needs to enter the war, which likely ends with Prussia and its German allies defeating both, with Hungary likely in revolt. Russia doesn't NEED to enter the war, but it'd be in their immediate geopolitical self-interest. Them entering the war means that Austria is not going to survive. If Prussia beats Austria on their own, Bismarck (who wanted a united Germany under Prussia that did not include Austria, because he wanted a united Germany under Prussian hegemony, which Austria would be able to prevent from completely dominating the empire) might let Austria off the hook with potentially just a few minor border concessions (not that he necessarily would, but he did want good relations with Austria after the Austro-Prussian War). If Russia gets in on the action, they can be the hammer making sure Austria, arguably Russia's biggest rival on the continent sans
maybe Britain, is no longer an independent empire posing a threat to Russian interests in the Balkans. In addition, this is an opportunity for territorial expansion, which is Galicia. Add in the good relations between Bismarck's Prussia and Russia, and you'd see why Russia is likely to enter this war with Prussia, because even though we can see it would go against Russia's long-term interests by strengthening Germany compared to OTL, Alexander II and other Russians can't see how this is going to come bite them in the ass. So while Russia doesn't NEED to join, if Austria is siding with France, Russia is going to side with Prussia.
Can Russia also get Czechoslovakia?
I would say Slovakia is possible, but Czechia more unlikely, as it had many germans and would be part of a Grossdeutschland.
I seriously doubt they could get either. Galicia is likely, but Slovakia would be considered an integral part of Hungary by many Hungarians. Thus, it probably stays Hungarian, unless Russia gets greedy (which I doubt, because they'd realize that would be asking for too much and would be handicapping themselves just by asking for it. They'd likely fail to get it and worsen their international prestige, especially in terms of relations with Hungary), so no. Czechia is 100% becoming part of Germany in this scenario. Hungary would likely be semi-independent with ties to both Russia and Germany. Initially they'd favor good relations with Russia, whereas long-term they'd likely become German allies due to Russian Pan-Slavism.
I also have a few questions of my own:
Who'd be an independent Hungary's king?
Assuming Spain joins Prussia in this war, what territories might they gain, how large an indemnity could they expect from France, and what effect would this larger indemnity have on the French economy?
Could Italy be compelled to join Prussia, what territories might they gain, how large an indemnity could they expect from France, and what effect would this larger indemnity have on the French economy?
And perhaps most importantly, how would Austria-Hungary plausibly join this fight?