Hmmmm... looking at that 'slopping liquid' idea. So basically, you convert nuclear energy into kinetic energy, then convert the kinetic energy back into electrical potential energy, then back to kinetic energy in a different direction? Problem: only the liquid's kinetic energy would be converted. You would loose the kinetic energy of the container, because you'd have to use thrust to slow down the container to make the liquid 'slop'.
Consequently, why not do away with the liquid entirely? It's just extra mass that plays no useful part, and because the energy conversions described are not 100% efficient, it actually has a negative effect.
Container and liquid are stationary. Container accelerates, moving the magnetic coil relative to the liquid thereby generating electrical energy. This means that there is a resistive force to the motion of the coil relative to the liquid (the accelerating force on the container must work against this force to generate power as well as giving kinetic energy to the container). This resistive force remains in effect until the liquid is moving at the same velocity as the container. The thrust energy has therefore been converted into:
* electrical energy in the magnetic coil
* kinetic energy in the container
* kinetic energy in the liquid
When thrust is applied in the other direction to counter the kinetic energy of the container the same thing happens again, except the kinetic energy gains in the two opposing directions cancel each other out. This is what happens with a conventional spacecraft. However, this one's thrust has twice generated electrical power in the magnetic coil. Because of this, its engine has delivered more energy than a standard spacecraft. The extra energy delivered has been converted into light and heat (as usual in a chemical rocket) and also electrical power.
So, the liquid system would have no effect whatsoever except to generate power from rocket thrust. There are more efficient ways of producing electricity from the chemical energy in rocket fuel.
Nice try, though. Took me some time to spot the flaw. The trick is to remember that energy is always conserved. If you think you're getting something for nothing, go through the energy equation with vector quantities, not scalars.