How modern were the armies and administrations of the Warlord Era (1916-1928) in China? What forces worked against the longterm solidification of these smaller regional states?

Don't know much about the Warlord Era myself, as my main thing is the Second Sino-Japanese War, but I can direct you to two leading English-based academics on military history in the Warlord Era.

Edward A. McCord is the leading scholar on the Warlord Era and two of his books, Military Force and Elite Power in the Formation of Modern China and The Power of the Gun: The Emergence of Modern Chinese Warlordism focuses heavily on military conflict and development during the 20s and 30s.

Kwong Chi Man is another scholar who specialises in this period. I have yet to read his War and Geopolitics in Interwar Manchuria: Zhang Zuolin and the Fengtian Clique during the Northern Expedition, but I do know his favorite warlord (!) is Zhang Zuolin so it promises to be a good book. If you want to know what a battle looked like at that time, I would recommend his 'Searching for Decisive Battle: The Shanhaiguan-Rehe Campaign during the Second Zhili-Fengtian War of 1924' in Decisive Battles in Chinese History, or 'Revisiting the Guo-Zhang War of 1925: From Military Perspective.' However, I think the above two works are in Chinese.