It's not a good sign when you ignore objective historical facts but to be fair it's clear that a lot of effort was put into this.
We're creating an alternate history mod where the Qing are still around. While I wouldn't say that we "ignore objective historical facts", we do make assumptions in order to rationalize certain outcomes. As I said earlier, in order to keep KR china recognizable, we decided that the preservation of certain elements was key. This involves some backwards-rationalization.
It's implausible that Sternberg could wrest Inner Mongolia even from a retreating Guominjun, as even if they were severely defeated, they would still have probably around 50k troops to his small army which would be unlikely to number more than 10k.
The Guominjun are meant to be significantly weaker in this timeline even before the Northern Expedition, their main army under Feng Yuxiang historically held off the Fengtian Army around Zhangjiakou thanks to Soviet aid, and in particular their construction of concrete fortifications. Without that aid the Guominjun never make serious inroads beyond Sanmenxia into Henan, and they're barely holding on in South Chahar. As Fengtian's armies rush south to deal with Wu Peifu's unexpected advance toward Beijing, Mongolian forces sweep in from the opposite site. We also make a blanket assumption that progressive movements like Feng's, no matter how genuinely progressive he actually was, are somewhat weaker KRTL due to the success of German militarism in Europe and the collapse of the Western democracies.
It's also hard to see how the KMT could have gotten as far as they did here with no Russian support. Chen Jiongming would probably have been able to defeat them on his own. I do not think a German military intervention was necessary to bring down the KMT here. A great example of what the KMT was capable of without foreign support can be found in their First Northern Expedition, where they were unable to take any of their objectives, were halted around 100 km from their starting point, and were unable to suppress Chen Jiongming without assistance from Yunnan. French advisors and some Bolshevik exiles would simply not be sufficient. The KMT OTL was unable to break out of this without Russian help because most of their money was used trying to bribe their warlord allies from attacking them.
The French are meant to have played quite an active role in supporting the KMT, one comparable to the Soviet Union OTL. It's not just advisors and Russian exiles, but also funds and weapons. Also, the KMT do mostly lose the war on their own, the Germans don't provide a ton of support.
There is no reason why the KMT being defeated would lead to the Sichuan Unification Conference actually amounting to anything more than it did OTL. I also don't see why Chen Jiongming would want to "restore" Lu Rongting, who was finished as a political force. He might have been able to defeat the New Guangxi Clique, but if he did, he would probably just annex Guangxi, rather than restoring an old enemy to power there who had nothing to offer or threaten him with.
It's harder for me to comment here because my area of expertise is really North China, but my understanding is that the rationale for Yang Sen's presence isn't so much that the conference was a success, but rather that he was selected and then backed by Beijing due to his Zhili ties. He's barely hanging on to de-jure leadership of the province, and gets thrown out in the vast majority of games.
As for Lu Rongting and Chen Jiongming, the idea is that Sun Chuanfang (and by extension Wu Peifu and the Germans) prefers to keep them at loggerheads, instead of creating a unified southern clique that could threaten his rule in Nanjing. They're set against each other, and also against Sun.
The biggest issue I have is that American mediation would probably not lead to a ceasefire on all fronts across China, and even if it did, it would not last long. Sun Chuanfang's provinces would reject rule by a Qing government in the north.
Well, it doesn't necessarily lead to a ceasefire on all fronts, just the movement of the main armies. With the timeline and the Northern Expedition writeup we're always covering the major actors, and assuming there's smaller scale action happening at a level that's less important for us to cover. Also, Sun's provinces do reject rule by Wu Peifu's government in the north. The state of "unification" is mostly de-jure, which is why we say that the Qing Government's control is mostly limited to the North China Plain.
Also, Zhang Zongchang joining Yiguandao, and actually letting them take over parts of his administration in Shandong, is unrealistic. He might join them as a hollow gesture, but I doubt that.
It is a hollow gesture. He doesn't see them as a serious problem, and considering the shockingly bad administrator he was, that doesn't seem unreasonable to me.
But in general, China remaining united peacefully for 7 years is absurd. There are many large factions that have no reason to trust each other, and their territories are not secure either, especially Shanxi. OTL, a united China that quite closely resembled this one lasted for about 8 months before the first major conflict started. It would be impossible for Wu Peifu to balance out all of his allies successfully for such a prolonged period of time. To be fair, Wu might want to limit his interference in his allies territories, which Chiang Kai-shek did not do, but this would not solve the underlying problem, that these factions are not dependent on the Qing government for anything, and war would start again soon.
It doesn't remain at peace for 7 years, there's the Shanghai Uprising, and presumably smaller conflicts between warlords. As for the major actors, you're right that the cliques aren't dependent on the Qing government, which is why(as I mentioned above) the "unification" is mainly de-jure. The primary factors preventing conflict between the major factions are:
1. The risk of starting a regional war. The situation in China resembles a sort of frozen conflict, where Germany and Japan are squaring off against each other, but benefit too much from the status-quo to start anything. Japan gets to keep a fairly secure Manchuria, agreed to by international treaty, Germany gets to subvert the Legation Treaty via the AOG, and the United States gets to formally uphold the "Open Door Policy" while taking its own share of the pie. The risk of the United States siding against an aggressor is also a major factor for either Germany or Japan. As a result there's a fair amount of pressure on the parties within China to uphold this status quo if they want to keep the aid they're receiving, and Sun Chuanfang (who is the nearest sub-national competitor to Wu in terms of strength) is particularly dependent on German aid. The natural thing for him to do would be to side with Zhang Zuolin against Wu Peifu, but German pressure makes that impossible.
2. The concentration of heavy weapons in only a few hands. Unlike OTL where China was subject to arms treaties making the import of heavy weapons difficult, those treaties don't exist in this timeline, meaning that the foreign-aligned factions in Beijing, Nanjing, and Shenyang are significantly better equipped than in the inland and non-aligned factions like Shanxi. This means that those smaller poorly equipped cliques will have a hard time banding together against the status-quo factions.
3. The Legation Cities. The main purpose of the "Neutral Zones" surrounding the Legation Cities, beyond providing them with protection, is denying the major warlord cliques the opportunity to exercise control over key logistical and financial centers like Tianjin and Shanghai. This reduces avenues for competition, and means that a major north-south war will need to take place almost solely on, or in the vicinity of, the Jinghan Railway - almost guaranteeing a stalemate.
Even with all this, though, China is meant to be like tempered glass at game-start. All it takes is some unrest and an assassination to send everything spiraling out of control. From there forward everything is game-design more than it's alternate history.