So, I wont be able to answer this question in full, mainly because anyone is gonna have a hard time finding maps of warlord-era China. It's just, as you said, a period of total chaos where China really is a failing state. I tried looking into it quickly online, but to no avail - I couldn't find any contemporary maps. I'm lead to believe that the best bet for anyone would be Japanese-based sources because, as I'll explain, Japan had a heavy hand in the chaos that engulfed China during this time. Unfortunately, I do not read/speak Japanese well enough to launch into that. That being said, I can answer parts of your question, especially the last "How much was known about internal politics by outsiders at the time?"

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When the Qing dynasty fell apart in 1911, the rest of the world did have an eye on China. China was a key region for European goods such as silk for clothings and soybeans for farmers, kind of like it is today. The nation with the most interests in watching this progress (and influencing it) was Japan, which for all intents and purposes by this point in history was considered Western by many Chinese nationalists. By 1922, another nation which was born into the world also looked down upon its southern neighbor with interest - the USSR. I'll break this response into two seperate parts dealing with Japanese interest and Soviet interest, and how they played an influential role in the way China would be formed.

Japan

In 1895, Japan defeated China for control of Korea, Taiwan, Qingdao and Port Arthur (Lushun). The event would lead directly to the outrage of a patriotic Chinese citizenry and the downfall of the Qing. From the moment the Qing fell apart in 1911 up to the beginning of WW2, Japan had a keen interest in keeping China isolated and dissolved. Japan's ultimate goal was, at this time, the unification of a pan-asian front, and China was the largest region to this ideological alliance. In the Northeast, or Manchuria, Japan directly played a role in politics by giving material aid to a bandit named Zhang Zuolin. Zhang would become the biggest puppet in Northern China for Japan until his assassination (by Japanese officers) in 1928. From there, Japan was successfully able to control the valuable soybean trade that exported massive amounts of beans to the West. In 1926, when the Northern Expedition kicked off in earnest, Japan deployed additional troops to Shanghai and Jinan, resulting in the Jinan and Shanghai Incidents (1928 & 1932, respectively), where Japanese forces attacked Chinese troops. After the KMT takeover of most of China, Japanese influence generally degrades in most areas, although in 1931 the Japanese do outright invade Manchuria. From 1928-1945, it really does become an off-and-on battle between the Republican KMT and the Japanese who are attempting to take control of China. Some speculate that later defectors of WW2, such as Wang Jingwei, may have been in contact with Japanese officials much earlier than one could assume.

USSR

The birth of the USSR meant the opportunity to export the revolution. Sun Yat-sen himself was somewhat of a socialist, but he never did identify fully as a communist. Most importantly though, both the USSR and the KMT were anti-imperialist organizations defending their homelands from what they saw as attacks by the West. From its founding to the end of WW2, the KMT would receive an egregious amount of materiel aid and funding from Stalin, as Stalin saw the KMT as a good way to protect Russia's flank from Japanese invasion. The USSR was also involved with direct invasions of Xinjiang after the near defeat of their puppet, Sheng Shicai, in 1934. So both the USSR and Japan, both ideologically believing to be helping China (though in very different ways) held Chinese puppets that supported their direct interests. Even after the 1928 Purge of the Communists by the KMT, Stalin continued to support the KMT as he knew only Chiang Kai-shek would be apt for the job of defending Russia's rear, which was most important to Stalin, especially after the Nazi takeover of Germany.

Other Powers

The USSR and Japan were the largest influences on Chinese politics in the warlord period, but other powers were certainly aware. In fact, Germany allowed several officers to be sent to China in order to train Chinese troops on modern weapons tactics. There is a flurry of correspondence between the UK and US about Japanese aggression against China, especially as it becomes more apparent that Japan will stop at nothing to unite East Asia. Everyone knew there was a huge power vacuum in China, that the KMT was mostly corrupt and weak, and that Japan was lurking at any moment to stab China in the heart. It was a dangerous time, with dangerous consequences.

Conclusion

I know this doesn't answer your questions about the maps in full, and that may not be answerable on a community like this, as primary sources from this time are rarely translated into English or available. Such was the chaotic nature of China where so many crucial historical documents are unnoticed, lost, or were destroyed. However, I do hope I did a good enough job answering some of your other question, particularly on foreign influence.

So in conclusion, yes the outside world knew very well what was going on in China during this period. The two major powers influencing these politics were the USSR and Japan. But after 1937, most of that didn't matter, as China was left to face Japan on its own for four years.

Sources:

Biography of Zhang Zuolin by Xu Che and Xu Yue (In Chinese)

Diplomacy and Deception: The Secret History of Sino-Soviet Diplomatic Relations, 1917-1927 by Bruce Elleman

Facing Japan: Chinese Politics and Japanese Imperialism, 1931-1937 by Parks Coble

/u/Drdickles and I had actually been discussing this question by PM, and at the time we both hit the same obstacle – it's really bloody hard to find contemporary maps of China! But since then, I've had a bit of a eureka moment and traced an alternate lead: world maps. In turn, this has led me to the David Rumsey map collection, an open-access database of high-quality digital map scans, including from several major atlases of the period. In turn, I was able to locate the specific China maps within those atlases, and one freestanding one. In all, I turned up 3 maps of China and 6 world maps printed between 1919 and 1928 (no doubt, there must have been more, these were just the ones I could find in around 45 minutes.) These were, in chronological order:

• 'The Official Map of the World' by L. V. Crocker, published by the National Survey Company in Chester, Vermont in 1919;

• 'The World, Prepared Especially for The National Geographic Magazine' by Gilbert Grosvenor, published in Washington D.C. in 1922;

• 'World - Political' and 'China - Southern Section', published by the Institute of Social and Religious Research in New York in 1923;

• '2. Weltkarte' (Map of the World) and '74. China' by Hermaan Haack and Adolf Stieler from the second edition of Stielers Handatlas, published in Gotha, Germany in 1925;

• 'The World Showing Principal Nations' Colonial Possessions' and 'China, Japan and Mongolia' from Atlas Of Prince Edward Island, Canada, And The World, published by the Cummins Map Co. in Toronto in 1925; and finally

• 'The New Map of the World', published by the Washington Square Book Shop in New York in 1928.

From the world maps, it's readily evident that they weren't just marking pre-Warlord borders, they were marking Qing borders! World maps produced during the late 19th century typically marked a clear internal border between China proper (the eighteen provinces as established by the Ming) and 'Chinese Tartary' or what have you – take this American nautical chart currently in the Hong Kong Maritime Museum. (Side note: if you're ever in Hong Kong, visit the Maritime Museum. This isn't an invitation, this is an imperative.) World maps of the early Republican period show the entirety of the Qing Empire as it stood in 1910 continuing to be lumped under the 'Chinese Republic', irrespective of actual separatist movements in Tibet, Mongolia and to a lesser extent Xinjiang, yet at the same time retain the marking of internal borders within the broader former empire. Hence Tibet, Xinjiang, Mongolia and Manchuria are generally marked out as sub-units of the whole. This continuity reaches somewhat absurd extremes, with the three world maps from 1925 and later showing Mongolia as part of China, despite it basically having become a Soviet satellite state since 1924. The sole exception to the trend of including Mongolia is the specific China map in the 1925 Canadian atlas, which shows it as a separate entity (also, interestingly, controlling the former Northern March of Xinjiang, which is now PRC-ruled), but Stieler and Haack's map of China marks only an internal border, as does the 1928 map from New York. Tibet, which was de facto independent until the 1950s, remains part of China on all three.

Irrespective of which map you look at, though, individual warlord cliques are never marked out. This is in part because while warlords exercised de facto regional military hegemonies and there were functionally no centralised government bodies to speak of, there was a relatively cohesive civilian world in the early Republic, and a continued diplomatic recognition of a central Chinese state based in Beijing, even if the specific government running it tended to be a little volatile. China ultimately became a belligerent power in WWI and dispatched the Chinese Labour Corps under the auspices one such Beiyang-backed figure, the old revolutionary leader Li Yuanhong. Basically, these maps seem to have been conveying de jure territorial claims as proclaimed by the (somewhat ephemeral) Republican governments, rather than seeking to convey the de facto political realities on the ground, and this manifested both at the broad geopolitical level as regards 'imperial' territories of the old Qing empire, and the smaller-scale clique politics below those top-level divisions.