Tom, it is no coincidence that the magnetic north pole is close to the geographic north pole. To the best of our knowledge, that has been true for a few hundred million years, aside from relatively brief intervals where the polarity reverses.
The main source of the magnetic is the molten iron alloy in the Earth’s outer core (NOT the mantle). It convects vigorously, driven mostly by heat flow as the Earth cools. It is also highly conducting, so a magnetic field will set up currents in it, and a mechanism called the dynamo effect will provide a feedback loop that keeps the currents going. The rotation of the Earth tends to organize the flow, and that is the reason the field tends to be nearly parallel to the axis.
Now for that “magnetized” fluid. I imagine you wanted an Earth analogue, which would be a conducting fluid. Such an experiment has actually been done many times (see, for example, this video). The rotating fluid will not be magnetized unless an external field is applied, at least for a short while. And without a source of buoyancy (such as heat flow) to drive convection, the current will rapidly die away as soon as the field is removed. Mars used to have a magnetic field, but it long ago cooled to the point that it couldn’t sustain a dynamo.
The solar wind has a strong effect on the Earth’s magnetic field in space, but only a very small effect at the surface. The flow of molten metals is indeed far from uniform, and sources of asymmetry include topography and compositional heterogeneity at the surface of the inner core and the core-mantle boundary.