In general, the laws of conservation of energy/momentum in the Jedi universe aren't really laws... more like gentle suggestions. They either don't matter, or the situation (because of the Force) is never a closed system which is a prerequisite for such laws to apply.
Case in point: Yoda didn't move when lifting Luke's X-wing. A Jedi once moved an entire Star Destroyer. Yoda/Sidious were throwing heavy stuff around during their duels.
As best as I can tell from EU, the Jedi merely coaxes the Force to move things, instead of moving them himself. Think of it as pushing the gas pedal - you apply a miniscule amount of force, and a multi-ton car accelerates 0 to 60 miles and hour in seconds. YOU don't push the car. Or touching a button on a remote, and an enormous explosion from bomb whose detonator was wired to the remote results. Or you remove a small control rod from a nuclear pile and get fission reaction going.
Where the Force gets or puts the energy that is consumed/released is never actually spelled out in canon. It's The Force. (so your answer about Palpatine is "we don't have any idea").
In more physics terms analogy, imagine a heavy sphere standing on a very very small indentation on a gentle incline. The indentation causes the sphere to remain at rest for now. That sphere has a ton of potential energy. If the indentation is small enough, the sphere can be pushed out of it with minimal amount of energy/effort on your part - yet that gentle push will start the sphere rolling, and transforming its enormous potential energy into a great amount of kinetic energy.