Yes, zero is a number; in particular, it is an integer.
When you count the number of elements in an empty set, the result is zero.
Radioactive decay is not about the size of the particle, but about the total mass of the particles (or, you might say, the number of particles). Our exponential model for decay is an approximation that does not take into account the fact that there are a finite number of particles of non-zero size, so it does not accurately give the real number of particles. In reality, the number of particles will eventually reach zero; once you get down to one, the next step will not be 1/2 particle, but either to decay or not, and sooner or later it will.
But in the model, it can't reach zero, because the model represents a real number that is repeated halved, which can be done forever.