  We present in this paper the discovery, properties, and a catalog of 1165
high redshift $6.5 < z < 18$ galaxies found in deep JWST NIRCam imaging from
the GTO PEARLS survey combined with data from JWST public fields. We describe
our bespoke homogeneous reduction process and our analysis of these areas
including the NEP, CEERS, GLASS, NGDEEP, JADES, and ERO SMACS-0723 fields with
over 214 arcmin$^{2}$ imaged to depths of $\sim 30$ mag. We describe our
rigorous methods for identifying these galaxies, involving the use of
Lyman-break strength, detection significance criteria, visual inspection, and
integrated photometric redshifts probability distributions predominately at
high redshift. Our sample is a robust and highly pure collection of distant
galaxies from which we also remove brown dwarf stars, and calculate
completeness and contamination from simulations. We include a summary of the
basic properties of these $z > 6.5$ galaxies, including their redshift
distributions, UV absolute magnitudes, and star formation rates. Our study of
these young galaxies reveals a wide range of stellar population properties as
seen in their colors and SED fits which we compare to stellar population
models, indicating a range of star formation histories, dust, AGN and/or
nebular emission. We find a strong trend exists between stellar mass and
$(U-V)$ color, as well as the existence of the `main-sequence' of star
formation for galaxies as early as $z \sim 12$. This indicates that stellar
mass, or an underlying variable correlating with stellar mass, is driving
galaxy formation, in agreement with simulation predictions. We also discover
ultra-high redshift candidates at $z > 12$ in our sample and describe their
properties. Finally, we note a significant observed excess of galaxies compared
to models at $z > 12$, revealing a tension between predictions and our
observations.
