Any particle cannot exist at two places at the same time. The position of a particle is indeterminate. This means that there is no single position associated with the particle. This is a theory deduced from Heisenberg's uncertainty principle.
Yes and no. Until you measure the location a particle does not have a location. There is just a probability that it is somewhere that is proven or disproven when you attempt to measure it. By measuring I mean interacting with that particle: shining light on it, measuring it speed, momentum, energy, position anything. Actually, most quantum mechanical weirdness is only vaguely understandable assuming that a particle is everywhere at the same time.