The solar wind speed, and other parameters, are all quite variable. Indeed, the solar wind did essentially stop, in May, 1999 (
The Day the Solar Wind Disappeared). I don't know where you might find a long-term plot on the web, but I'm sure there is one somewhere if you poke around.
The volume of space dominated by the solar wind is called the
heliosphere, the boundary between the heliosphere and interstellar space is the
heliopause. The solar wind slows suddenly to sub-sonic speeds, creating a
termination shock. Beyond that, there is a
solar bow shock, where the
interstellar medium is slowed by the solar magnetic field. It's all quite a complex affair. The Earth's magnetosphere behaves in much the same way, and we assume that the solar magnetosphere is a scaled up version of Earth's, there being no good reason to assume otherwise. The shocks and boundaries of the Earth's magnetosphere are well mapped and observed (and also quite variable in location and intensity). The heliopause, on the other hand, is as yet not directly observed, at least not unambiguously. Before Mars became big news, the Voyager I spacecraft may have passed through the termination shock of the solar wind (
Voyager Spacecraft Approaches Solar System's Final Frontier).
There are electric currents flowing all over the solar system, quite as one would expect. the solar wind is a plasma, and magnetic fields can separate charges (electrons, being less massive, are more easily distracted by magnetic fields than are protons). The use of the term
Birkeland current is just bad semantics on the part of the electric cosmos folks, who apply the term indiscrimanently to anything that vaguely resembles a terrestrial Birkeland current. Not all current in space are Birkeland, and most aren't, although some might properly be called that. For instance, there is a steady current loop between Jupiter and it's moon Io (
The Io Dynamo). The solar magnetic field, driting with the solar wind, drapes over a cometary plasma, giving active comets a magnetoseath.
It's all quite complex, and there is no easy one-page answer to questions about magnetic fields and electric currents in the solar system. In general, the study of such things comes under the discipline heading of
space physics or
space plasma physics (in Europe more than the U.S.A., they like
space science), and those are the proper literature/web search keywords. I recommend the online
Oulu Space Physics Textbook as a good place to start. You can also try NASA's
The Exploration of the Earth's Magnetosphere, or the
education links from NASA's
Sun-Earth Connection program.