It happens everywhere, yes. Do note these "virtual particles" do not behave completely the same as real particles. They are more conceptual descriptions (they are not directly observable, except for the effects they can cause). If you treat them the same as particles it will appear as if they violate some fundamental laws.
But the basic idea is that each fundamental particle has a field that it belongs to (e.g. photon field aka electromagnetic field, electron field). These fields stretch out in all dimension, with a total energy of 0 (except the higgs field). An excited state in such a field is a particle.Virtual particles are the fluctuations in these fields. The energy of these fields are quantized (quantum!), similar to integers in math, e.g. there's 1 2 and 3, but not 1.2 1.3 1.5 etc.
As for the unpredictability thing, I like to think of it like this: Suppose you have a dice that you roll an infinite number of times. There is no pattern to it, nor does it appear to have one most of the time. But at some point you might roll the same number thousands of times in a row. It might appear as if the dice is flawed somehow, but this is just something that might happen in such a random process. As for the universe, we are not seeing all of the permutations that did not lead to the state we are currently in. The chance that you exist is incredibly small, but if this randomness goes on for long enough (infinitively), it will happen again and again. This is similar to the evolution of species, you only see the "winners".
But the basic idea is that each fundamental particle has a field that it belongs to (e.g. photon field aka electromagnetic field, electron field). These fields stretch out in all dimension, with a total energy of 0 (except the higgs field). An excited state in such a field is a particle.Virtual particles are the fluctuations in these fields. The energy of these fields are quantized (quantum!), similar to integers in math, e.g. there's 1 2 and 3, but not 1.2 1.3 1.5 etc.
As for the unpredictability thing, I like to think of it like this: Suppose you have a dice that you roll an infinite number of times. There is no pattern to it, nor does it appear to have one most of the time. But at some point you might roll the same number thousands of times in a row. It might appear as if the dice is flawed somehow, but this is just something that might happen in such a random process. As for the universe, we are not seeing all of the permutations that did not lead to the state we are currently in. The chance that you exist is incredibly small, but if this randomness goes on for long enough (infinitively), it will happen again and again. This is similar to the evolution of species, you only see the "winners".