If all scientific knowledge were destroyed and one sentence could be passed to the next generation, it should be that all things are made of atoms: little particles in perpetual motion, attracting when a little distance apart and repelling when squeezed together. Feynman argues this single hypothesis contains an enormous amount of information about the world if applied with imagination and thinking.
In physics the test of all knowledge is experiment; experiment is the sole judge of scientific truth, not authority or reasoning alone. The source of knowledge is also experiment, which both suggests new principles by giving hints and confirms or refutes the imaginative guesses that reason constructs from those hints.
The conservation of energy states that there is a numerical quantity which does not change through any process in nature; whatever happens, if you compute this number before and after, it is identical. Crucially, we have no knowledge of what energy actually is; it is an abstract formula, a set of terms that we add up, with no mechanical picture of the thing being conserved.
Discovering the laws of physics is like watching a chess game you do not know the rules of and trying to infer them from observing the moves. You can sometimes deduce a rule from one corner of the board without understanding all the pieces, and a single apparent exception (like castling) can later force you to revise a law you thought you knew.
A tiny particle suspended in water, viewed under a microscope, jiggles endlessly in a random dance. Feynman cites this as direct evidence of atoms: the visible particle is being struck unevenly by the ceaseless motion of invisible water molecules, so its jitter makes the atomic hypothesis observable.