The answer to all these questions, in a super-fast, slightly disingenuous, and very un-nuanced way, is "because Mao Zedong won history". Out of all the single-party dictators who emerged out of the 20th century crazy, all ruling with censorship, personality cults, and violence, the Chairman emerged relatively unscathed, even though, let's face it, he did not have a light hand with doling out punishment. While "Hitler" is now synonymous with "evil" even to German people, Mao's granddaughter peacefully calls grandpa "a symbol of revolutionary culture". Nikita Khrushchev spent a considerable amount of energy candidly removing Stalin's cult of personalty, but my 1990s experience suggest that the same wasn't done for Mao in China. Japan's Hideki Tojo was sentenced to death at the International Military Tribunal for the Far East, but Mao's face is still on a T-shirt. Even Mao's own wife could not retire gracefully from her political life.
To speak about someone like Mao without nuance in today's academic society is to flirt with danger. To paraphrase a real historian (not a wannabe one like myself), China is bigger, older, and more powerful than just about anyone else right now, Orientalism dictates that we shall treat this "other" society and its people with some type of exceptionalism. In other words (to paraphrase myself), it is currently trendy not to hate Mao. Gone are the days of "reds under the beds" or the speak bitterness campaigns about the excesses of the Cultural Revolution.
On another level, the appropriation of Mao's image has something to do with the now socially-acceptable attitude to socially-accept Mao with only a little reservation. It is not completely fair to compare Mao's legacy to that of Hitler or even Stalin, because Mao's image after his death became a carefully curated, useful tool to maintain social stability in the face of heavy economic and political reforms. In my view, this more closely resembles the exemption of the Japanese emperor Hirohito from the Military Tribunal in the aftermath of the Pacific War -- with the Japanese society in flux, the consistency of the imperial family's sanctity was maintained.
Mao's pervasiveness in Chinese culture (and indeed, that of the world) has become obscured with the impossibility for Chinese people to remember the 1950s and 60s without the official line, its sound-bites and its new canon. When Mao left behind his writings, a formidable collection of his likeness in propaganda art, and a country that needed to reform, and fast, he won history by leaving his successors no choice but to write it like he was writing it himself.