I understand that the Russians surprised the Central Powers with a far quicker mobilization. But the Germans quickly managed to turn things around. A hundred years ago they had destroyed one Russian Army and are in the process of badly beating another one. Meanwhile the Austrians are doing extremely badly against the Russians. The Russians are managing to push 160 km into Hungary and the KuK military is suffering huge casualties.
The comments I read about the poor performance of the KuK troops usually talk about the whole war. Which includes things like production/industrial issues and low moral of the multi-ethnic troops. But I'm specifically concerned about 1914 and the initial phase of the war, when production shouldn't be as important as in the long run and at least the core of the army should consist of professional troops.
So: Why Did Austria-Hungary Do So Badly Against Russia in 1914?
The Austro-Hungarian Empire during the period had real troubles even mobilizing it's armies. One of the most important factors that you mentioned before was the multi-ethnic composition of its armies. There was no universal language in the Empires army most of the time and different ethnicities were organised into different battalions/regiments etc. This made coordinating attacks and movements absolutely horrific and it also helped inflame the racial tensions within the army. The Empire had certain regiments that performed rather well (Many Hungarian one's come to mind) but overall its troops were ill-equipped, ill-trained and ill-led, nothing compared to their German neighbours. Combined with early mishaps in the war these troops were always likely to give up rather than press the attack.