a) In short, yes. The Japanese had been playing proxy games in China for decades. They had a vested interest in stemming the rise of a unified state, even if that meant full-on intervention.
In regards to China, yes. Japan decided to take up the position of head of East Asia from China after the European powers turned it into their playground. In their paranoia to avoid being next, they decided to become a great power themselves then proceeded to expand their influence to remove the Europeans from the region. I think you can call it "victory disease" after they beat Russia that made Japan so militant (although WWI and the depression didn't help matters).
Japan invading the DEI was just so they could continue their campaign in China. Invading the DEI (while it would have happened eventually) was largely in response to the US issuing an oil embargo on Japan in response to what was happening in China. The hard part for you is going to be getting the US involved eventually since Japan won't be reliant upon them for oil.
I don't believe it is at all certain that we will see a total war between China and Japan given a PoD in the First World War.
It is true that Japan struggled to become the strongest regional power between 1868-1945, but that doesn't necessarily entail total war with China, much less with the Chinese, Dutch, British, and Americans. After all, I think it's possible to say that it was a longstanding part of German national policy to dominate "middle Europe" and, if possible, expand to the East. But this doesn't mean that any government that comes to power is going to launch a world war in order to attempt it.
For Japan's part, the nation had long carved out concessions in China, following the example of the European powers (including the treaty ports opened in Japan until 1899, which ironically meant for a year or two Japan both operated and suffered under the treaty port system). But Japan did not constantly and consistently maintain the same policy towards China during this entire 80-year period. In 1895, Japan gained at the expense of China via outright war. In 1915, Japan tried to influence China via the 21 Demands (which backfired horribly). Later during the war, she issued the Nishihara Loans, which were more sucessful. After the war, she supported the Anhui Clique. All of these are ways that Japan might attempt to gain influence in China without outright war and conquest.
And, of course, Japan
DID NOT always try to expand its power and influence in China. In 1922, Japan agreed to give up all but purely economic rights in Shandong, abandoning all political and military rights there. In 1928, under the liberal internationalist FM Shidehara, Japan pushed for tarriff autonomy for China. This was something that China dearly wanted, and also something that the British and US opposed at the start of the meeting. If not for Shidehara, China likely would not have received tarriff autonomy at that meeting. For much of the Taisho Period, Japan was prosperous and relatively satisfied. After the long, painful experience of the Siberia Expedition finally ended, the military and military adventurism was unpopular with the Japanese public. This can be seen in the foreign policy that Japan pursued at the time--Shidehara's pro-Chinese policy, agreeing to naval restrictions, etc. Of course in OTL we know which kind of outlook and foreign policy won out. But that was not the only foreign policy the Empire of Japan had practiced. There was not one, unified national plan from 1868-1945. With a PoD 20 years or more before the Second Sino-Japanese War started in OTL, who can say what butterflies will be seen?
For the specific PoD of a Japanese DEI, I could see it going either way. On the one hand, it may make Japan more self-sufficient, and thus allow Japan to take a tougher stance earlier if they so desire. On the other hand, it makes Japan more self-sufficient. The "Strike North" plan was about securing a long-term buffer or defensive perimeter for Manchuria. The war against China was partly about removing or at least putting off the possibility of a strong China that could rival Japan. But I would argue that the larger part was simply a desire for resources. Auturky was a central tenet of the beliefs of the Militarists, as it was for other far-right governments of this time. Therefore seizing the resources of China, both material and people (as consumers or laborers) was seen as vital. There was a desire to turn it into a "Japanese India". Here, we might actually seen this idea as
lesspopular, as Japan would already be self-sufficient in oil and has the resources of these islands at its disposal. So the perceived pressure might actually be lower. Finally, the DEI is very far from the Home Islands. The IJN of 1918 is not up to the task of defending it. It will have to be transformed from a fleet that can defend the Empire and its immediate surroundings into a force that can travel as far as the Indian Ocean in order to defend the DEI and vital oil shipments from those islands. Therefore we would likely see the IJN with much larger relative budgets, and it would gain prestige and influence at the expense of the IJA. So IJA ideas like expanding on the Asian mainland would be less likely to be taken up, I think.
Of course, I want to stress again that I think with a PoA of 20 years or mroe before the events we are talking about, almost anything is possible.