#5, this concept of general skepticism and confirming your own facts was echoed -- I don't know if it was conscious -- by Thomas Jefferson in this famous quote:
Fix reason firmly in her seat, and call to her tribunal every fact, every opinion. Question with boldness even the existence of a God; because, if there be one, he must more approve of the homage of reason, than that of blindfolded fear.
The quote comes from a letter Jefferson wrote to his nephew giving general life-lessons and advice. The advice seems very similar, saying that you cannot know anything unless you take the time to research it and make your own decisions; don't let biased opinion influence you.
I think the social implications are very helpfully pointed out in #6 is particularly important to focus on. The Buddah created a new religion that focused on other-worldly aspects of life that represented a sharp divergence from the centrality of the Indian caste system to Hinduism. By focusing on englightenment and not on such earthly measures, it is a very different religion.
The Buddha showed people a clear path to achieving spiritual benefits, also promised by Hinduism, without the rigid class structure and hierarchical implications of that religion. It was, and is, in many ways a result of Siddhartha's desire to separate the human condition from what seemed to be inherent to it: suffering.
Siddhartha Gautama also eliminated the importance of class distinction in spiritual matters, essentially walking away from his own rank and leading others to do the same.
In a society with a caste system that works/worked in conjunction with the philosophical view of reincarnation as a reality (where your spiritual status on earth determined the level of your re-birth), the Buddha was making a big break with custom by choosing to be a possessionless monk.
Buddha told his followers, "Don't believe anything anybody tells you, including anything I tell you, unless it agrees with your own experience and your own common sense." The common sense of Buddhism is what makes it so attractive to many people. All the Hindu gods are obviously fantasies and do not agree with common sense. Buddha had a conventional education but tried to extra what was of practical value from all the superstition and mythology he had been taught. Unfortunately, a lot of superstition ,mythology, and rituals have attached themselves to Buddhism since his death.
Buddha emphasized the ability to attain peace in this life rather than through a series of reincarnations; his emphasis, in general, was more "this-worldly" than the general emphasis on Hinduism, which is why he did not consider deities essential.
Buddhism eliminated all the gods (or all of the variations on one god, depending on how you see Hinduism). Instead of worshipping a god or gods, Buddha focused on trying to get rid of the desires and wants of the world. This is a very different approach to religion.