A towed large, wire, multi-turn, loop traveling orthogonally to the field, would seem to me, likely to generate an emf.
Yes - this can be done and has been demonstrated a number of times in the past (including as a space shuttle payload on STS-75). These tethers have been shown to generate measureable electrical power, but at the expense of additional "drag" on the satellite. I think the same method has been proposed as a de-orbit mechanism for small LEO satellites at the end of their life; a tether can be deployed which interacts with the magnetic field and produces a small force which over a period of a few years would lower the orbit enough for atmospheric re-entry.
See http://en.wikipedia.org/wiki/Space_tether_missions and http://www.iadc-online.org/Documents/IADC-06-08.pdf for more details.
Yes, as stated by Paul Eccleston above. I worked on the Tethered Satellite System Program (TSS) and it was very successful. He pointed out the "drag" due to conversion of kinetic energy to electrical. I also wanted to point out that atmospheric drag will also need to be carefully considered since you mention "very low earth orbit". Also, in very low earth orbit the effects of atomic oxygen on any spacecraft materials will need to be considered as the levels are higher in low earth orbit.
A tether has in fact been tested successfully and generated power on STS-75 as mentioned above. At one end of the tether was a satellite supplied by Italy that collected electrons. These electrons flowed down to the Orbiter and were ejected by an ion gun. The current was closed through the space plasma itself, which served as a sort of "electron reservoir". This process generated power and drag as mentioned above. However, if one were to add power to the system and reverse the current direction, the electrical force can provide a positive force and propel the spacecraft into a higher orbit.
Yes you can. In LEO, the orbital motion generates about 200V/km of electric field, and then you rely on the ionosphere to close the loop. Current closure was demonstrated on both STS-75, as well as PMG (bidirectional), however there are no correlated measurements of current and drag/thrust (although there is little doubt that the physics works).
Yes, it can be done in principle and has been demonstrated in space. The system is usually referred as electrodynamic tether, see the website: http://en.wikipedia.org/wiki/Electrodynamic_tether. However, there are still technical challenges to be solved before it can be used as power generator in space practically, such as the effectiveness and efficiency of plasma contactor to collect/emit electrons, the tumbling of the electrodynamic tether when it generates power.
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