Your chronology and facts are off here. Although it is difficult to pin down an exact start date for the Russian Civil War, it roughly started in November/December 1917 and only really began in earnest the following year. The Russian Army had begun a process of desertion and demobilization (sanctioned and unsanctioned) in the aftermath of the earlier February Revolution in 1917. But for all of the problems of tsarist Russia in the war, the army really was the last Romanov institution to break in the tumultuous revolutionary year of 1917. The Duma, the peasantry, the urban workers, and a myriad other social groups and institutions turned against tsardom before the military began its protracted disintegration.

In the meantime, the political health of the Austro-Hungarian Empire was not that much better than that of tsarist Russia. The Dual Monarchy's military suffered a series of reverses, such as the Siege of Przemyśl in which the failure of the relief effort and the surrender of the garrison severely damaged the Empire's morale. The Austro-Hungarian war economy was sputtering as well, especially as fighting on the frontiers of the Empire created an internal refugee crisis. Food became quite scarce in the Empire's cities, and when the Austrian Minister-President Karl von Stürgkh was assassinated while at lunch in 1916 there was very little public sympathy for a man that many blamed for the Empire's food crisis. Ethnic relations within the Empire, never the most stable to begin with, began to fall apart with the spectre of national separatism emerging.

Germany did not nearly have so many problems as its Habsburg ally, and many on the German military and government saw the Russian Revolution and the makings of the Civil War as a godsend. In negotiations with the Bolsheviks, a faction willing to negotiate the end of the war, the Germans dictated the Treaty of Brest-Litovsk which would have reduced much of the western Russian Empire into independent vassal states dependent upon Germany. Although the negotiations for Brest-Litovsk were complex, Lenin agreed to them in the gamble that Germany lacked the manpower and resources to enforce this Carthaginian peace and would likely lose the war in the Western Front. Lenin's calculated risk proved correct. Although the Germans and their Central Power allies did try to carve out their own fiefdoms out of the corpse of the Russian Empire, they really could not keep this territory. The relative freedom of movement of the wartime German Ober Ost troops and the postwar Freikorps does testify to the overall collapse of Russian authority during the Civil War. Many of the German paramilitary formations used wartime stocks of materials and offered themselves up as freebooter companies to the Whites while their leadership toyed with carving out a neo-Germanic state on the Baltics. Such dreams were unrealistic and these German military units could not form a lasting political order or government over this largely non-German population. Many of the Freikorps ended up ejected from their would-be conquests. If it was impractical to occupy the Baltics, then Moscow, where the Bolsheviks had relocated the capital to in 1918 because of Petrograd's proximity to the fighting, was simply out of reach.