We report on a full-polarization analysis of the first 25 as yet non-repeating FRBs detected at 1.4 GHz by the 110-antenna Deep Synoptic Array (DSA-110) during commissioning observations. We present details of the data-reduction, calibration, and analysis procedures developed for this novel instrument. Faraday rotation measures (RMs) are searched between $\pm10^6$ rad m$^{-2}$ and detected for 20 FRBs with magnitudes ranging from $4-4670$ rad m$^{-2}$. $15/25$ FRBs are consistent with 100% polarization, 10 of which have high ($\ge70\%$) linear-polarization fractions and 2 of which have high ($\ge30\%$) circular-polarization fractions. Our results disfavor multipath RM scattering as a dominant depolarization mechanism. Polarization-state and possible RM variations are observed in the four FRBs with multiple sub-components. We combine the DSA-110 sample with polarimetry of previously published FRBs, and compare the polarization properties of FRB sub-populations and FRBs with Galactic pulsars. Although FRB polarization fractions are typically higher than those of Galactic pulsars, and cover a wider range than those of pulsar single pulses, they resemble those of the youngest (characteristic ages $<10^{5}$ yr) pulsars. Our results support a scenario wherein FRB emission is intrinsically highly linearly polarized, and propagation effects can result in conversion to circular polarization and depolarization. Young pulsar emission and magnetospheric-propagation geometries may form a useful analogy for the origin of FRB polarization.
Comment: 57 pages, 24 figures, 5 tables ; version accepted by ApJ ; revised classification to include polarized signal-to-noise; added appendices for PA error/variability, J1935 polarization ; corrected literature FRB sample and supplemented with omitted data; added discussion of biases, limitations, and selection criteria; revised sigmaRM analysis ; additional plots added ; revised FRB20220424E analysis