Short answers, pulled from the story.
The invariable plane is the plane passing through the Solar System's barycenter, perpendicular to its total angular momentum vector. It represents the weighted average of all planetary orbital and rotational planes and is also called Laplace's invariable plane.
The invariable plane is named after the French astronomer Pierre-Simon Laplace, who called it the "plane of maximum areas." Laplace defined the "area" as the product of a body's orbital radius, its radial velocity, and its mass.
The invariable plane is fixed for the entire planetary system and is derived from the sum of all angular momenta across every body. The Laplace plane is specific to individual satellites and describes the plane around which a satellite's orbital plane precesses. The two are equivalent only when all perturbers and resonances are far from the precessing body.
The invariable plane lies within 0.5 degrees of Jupiter's orbital plane, calculated at precisely 0.3219 degrees. Jupiter contributes 60.3% of the Solar System's total angular momentum, making it the dominant influence on the plane's orientation.
The four giant planets contribute about 98% of the Solar System's angular momentum. Jupiter leads at 60.3%, followed by Saturn at 24.5%, Neptune at 7.9%, and Uranus at 5.3%.
Real bodies are non-spherical, and tidal friction allows a small transfer of angular momentum from axial rotation into orbital revolution. External influences such as Milky Way galactic tides and passing stars also exert tiny torques. These effects cause small changes in both the magnitude and direction of angular momentum, though the changes are exceedingly small relative to the system's total momentum.