It's so common place now for big corporations to spend millions every year on acts of goodwill and charity. How long have corporations been doing it for? How did it become a standard business practice? Surely, I would assume, it was initially viewed as a waste of money.
Moreover, when did people start getting skeptical of these acts? What are some early examples of PR disasters that corporations faced?
To start off, Edward Bernays (1891-1995), a nephew of Sigmund Freud, is commonly referred to as the founder of modern public relations, in the U.S. at least. He took the elements of propaganda—used with nationalistic success during World War I (and later in World War II)—and applied them to the business world. In addition to operating a PR firm during the 20s with his wife, he authored several books from 1923 to 1955, the early ones of which focused on propaganda, transitioning to PR in the latter.
His first large success in the PR field was the "Torches of Freedom" campaign for Lucky Strike Tobacco, which helped make cigarette smoking socially acceptable for women by having them light up during the 1929 Easter Parade in New York.
That said, other efforts of what might be termed "public relations" existed before; the History of Public Relations page on Wikipedia goes rather in depth, with many good footnotes and links.
To answer them main gist of your question then, drawing from the above page,
In the 1930s, the National Association of Manufacturers was one of the first to create a major campaign promoting capitalism and pro-business viewpoints. It lobbied against unions, The New Deal and the 8-hour work-day. NAM tried mostly unsuccessfully to convince the public that the interests of the public were aligned with corporate interests and to create an association between commerce and democratic principles. During the Second World War, Coca Cola promised that "every man in uniform gets a bottle of Coca-Cola for five cents, wherever he is and whatever it costs the company." The company persuaded politicians that it was crucial to the war-effort and was exempted from sugar rationing.*
* Coca-Cola reference: https://books.google.com/books?id=bSAChoqpnHUC&pg=PA249
I also found a reference in a 1940 edition of California and Western Medicine: Journal of the California Medical Association, calling for the medical science field to cease using the term "office of public relations" and instead use "office of good will." This seems to indicate that, even in by 1940, some corporate fields had found they needed public good will to survive and operate (the tone of the above editorial suggests the medical/research fields were a latecomer to this understanding). Bernays, in Public Relations, calls the field of PR "a form of social statemanship."
As for the last part of your question, that's a little out of my immediate knowledge (I graduated recently in journalism, and we touched on this history briefly); I hope other experts can chime in and help flesh it out.
EDIT: Had a dyslexic typo on Bernays' year of death.