The weakening of the field to zero then the strengthening lets in more charged partciles then normal. None of this is instaneous, its not fliping a light on and off. This “changing” leads to inceasing then maximizing then decreasing cloud cover, it has to effect glaciation events.
yes though the whole chicken and egg thing kind of applies here. Its possible solar changes, or meteor impacts lead to the magnetic field changes, or glacial changes related to the distribution of water around the planet affect its as well.
They are all clearly related, but which if any came first is unknown.