The vacuum is important because any deflection of the alpha particles would only be because of collisions with the gold foil and not due to deflections off anything else
The fact that most alpha particles went straight through the foil is evidence for the atom being mostly empty space
A small number of alpha particles being deflected at large angles suggested that there is a concentration of positive charge in the atom - like charges repel, so the positive alpha particles were being repelled by positive charges
The very small number of alpha particles coming straight back suggested that the positive charge and mass are concentrated in a tiny volume in the atom (the nucleus) - the tiny number doing this means the chance of being on that exact collision course was very small, and so the 'target' being aimed at had to be equally tiny
Scientists cannot tell when a particular nucleus will decay, but they can use statistical methods to tell when half the unstable nuclei in a sample will have decayed