Re: anti-particles "moving backwards in time" ?
If you look at the mathematics of a photon scattering off of an electron you have to include a term containing positrons. This is a mathematical construct. It is true that the mathematics of a positron are that of an electron traveling backwards in time. Feynman diagrams are merely a computational aid to writing down the correct quantum field equations. If you look at the rules an antiparticle acts like a particle traveling backwards in time.
But this is just the mathematics. The physics content is the identification of a mathematical construct with a physical "reality". You start with a physical situation, map it into the appropriate mathematical construct, perform mathematical operations, and map the result back to a physical situation. The intermediate calculations don't map to reality - especially in quantum field theory.