Not precisely, Yorda, The Buddha's realization was about everything being directly connected, everything is one, and self is an illusion, so self doesn't simply go through amnesia and occupy another body, it's more of a big picture, like the tree of life. You were never in another body, the thing you call you is a one time deal. But, since everything is one, our ideas, our culture, our understanding or lack of it is inherited. There is a continuous transition between self and other, through the birth process. In a sense it's all one body that gets renewed over and over.
Reincarnation isn't an article of faith, but an implication of the essential truth that enlightenment reveals, that of all forms being a temporal manifestation of one thing. Want to know about your past life? Study human history.
Buddha said life is suffering to counteract the idea that there is an existential problem in the fact that there is suffering in the world. The capacity to suffer, and the capacity to enjoy life both come from the same source, sensitivity. You can't have one without the other. But, most suffering isn't physical, it's mental, and that's what the Buddha's teaching works on.