Answer 1:
There are some ideas in quantum field theory about particles than can appear and disappear randomly. One of the basic aspects about quantum mechanics is that quantum effects are probabilistic in nature. Perhaps the most talked about case of this is the waveparticle duality nature of light. In any case, there are different types of particles that are continuously being formed and destroyed. Their random appearance and disappearance has roots in the "Heisenberg Uncertainty Principle" where it can be shown (theoretically) that there is a nonzero probability that the event can happen, and so it does. Now, for the case of a small organism  I suppose there may be a nonzero probability that an organism could appear or disappear, but the probability would be infinitesimally small. In fact, the probability of an atom (or even an electron) farther than a few nanometers away would be infinitesimally small as well. What may be of some interest to you on a related note is the idea of transferring information rather than atoms themselves. This works on the idea of quantum entanglement. There was some interesting work done at NIST on quantum entanglement that you could research and read up on if you're interested.
Hope this helps,
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