Does having a basement level increase overall earthquake resistance of a high rise building? Does it also lessen the burden on pile foundations?
Not necessarily, conventional earthquake-resistant high risers are designed considering the height of the structure the total height from the foundation to the roof, basically considering any underground stories as part of the structure unless for some special cases such as marine structures or high subterainean water level the lower part of the structure is contained in a big subterainean box.
In theory, it could be studied if designing the structure as a flag pole to take advantage of the subterranean part of the structure as a deep foundation that helps absorb some of the forces of the earthquake, albeit with an eye on the accentuated shear forces at the ground level floor, provisions for designing the first-floor connection to surrounding grade, and also additional stiffness of the building possibly absorbing high-intensity stresses during an earthquake. I am not aware of any building designed as such.
Modern active tall building seismic design is a different paradigm that is outside of the scope of this answer.
As for the underground floor helping to reduce the load on the foundation, again, it would make sense to think the void is lighter than the earth it replaces, although it adds the weight of a new floor, however in practice this is not considered unless specifically rocommended by approved soil and geology report.