Throughout the 1930s, it appears from a cursory glance that much of Japanese foreign policy was conducted on an ad-hoc basis in China by the Kwantung Army with the begrudging support of the civilian government. What grand strategy or endgame did decisionmakers have as they began expanding in China? Specifically, did military planners foresee a long, protracted war in China, were there any efforts to collaborate or use political forces in Republican China, and how did they envision a path to victory in the Chinese theater?
You might find my previous answer, linked here to be helpful. While less focused on the actual strategy employed in China, it should explore some of the topic you're interested in.
However, to give a quick tl;dr summary: when the Second Sino-Japanese War begin in 1936, Japanese leadership envisioned a short, sharp, war that would enable them to settle their disputes over the resources of northern China quickly and in Japan's favor. At first, the Japanese aimed to seize control of north China and destroy Nationalist field armies in order to negotiate from a position of strength. However, as Chinese resistance steepened, and Chiang Kai-shek's government refused to accept the Japanese terms (terms which would have likely been unacceptable to the Chinese population had Chiang's government accepted it), Japan's efforts to accomplish this changed. When defeating Nationalist field armies failed to bring Chiang to the table, Japan aimed to seize the economic heart of the Nationalist government. When that failed, the Japanese sought to close off Chiang's access to foreign aid, which ultimately was a major factor in the decision to go to war against the United States and the European colonial powers. It's difficult to say that there was any one "vision" for what the endgame of the war in China was to be, as Japanese ideas on what their desired "Co-Prosperity Sphere" would be were --in many ways--still in development as the war progressed.
I don't think my linked answer goes too into depth on the question of government in occupied China, and it's not a topic that I'm particularly knowledgeable in. However, suffice it to say that the Japanese absolutely did attempt to use collaborators and political divisions to manage their portions of China. There were a plethora of provisional governments set up throughout China by the Japanese, but the famous of which is undoubtedly Wang Jingwei's "Reorganized National Government of the Republic of China". Wang was a leader among the left wing of the Nationalist Party, Wang had been a rival to Chiang Kai-shek throughout much of the Republic's early days. However, as the war developed, Wang became convinced that the war against Japan could not be won, and so it would be better for all of China to cease the struggle, and instead attempt cooperation with Japan--at least until the point where China would be ready for a war with Japan.
I hope this helps to answer your question. Please feel free to ask any follow ups you may have.