Shapely versions < 2.0 load a GEOS shared library using ctypes. It's not uncommon for users to have multiple copies of GEOS libs on their system. Loading the correct one is complicated and shapely has a number of platform-dependent GEOS library loading bugs. The project has particularly poor support for finding the correct GEOS library for a shapely package installed from PyPI into a conda environment. We recommend that conda users always get shapely from conda-forge.
Generally speaking, shapely's predicates and operations are derived from methods of the same name from GEOS and the JTS Topology Suite. See the JTS FAQ for references describing the JTS algorithms.
The buffer algorithm in GEOS is purely two-dimensional and discards any Z coordinates. This is generally the case for the GEOS algorithms.