  We present our chemical abundance investigation of the metal-poor
([Fe/H]=-1.60 dex), r-process-enriched ([Eu/Fe]=0.73 dex) halo star HD 20 using
novel and archival high-resolution spectra at outstanding signal-to-noise
ratios. By combining one of the first asteroseismic gravity measurements in the
metal-poor regime from a TESS light curve with non-LTE analyses of iron lines,
we derive a set of highly accurate and precise stellar parameters. These allow
us to delineate a chemical pattern comprised of solid detections of 48
elements, including 28 neutron-capture elements, which establishes HD 20 among
the few benchmark stars that have almost complete patterns with low systematic
dependencies on the stellar parameters. Our light-element (Z<30) abundances are
representative of other, similarly metal-poor stars in the Galactic halo with
contributions from core-collapse supernovae of type II. A comparison to the
scaled solar r-pattern shows that the lighter neutron-capture elements
(37<Z<60) are poorly matched. In particular, we find imprints of the weak
r-process acting at low metallicities. Nonetheless, by comparing our detailed
abundances to the observed metal-poor star BD +17 3248, we find a persistent
residual pattern that is indicative of enrichment contributions from the
s-process. We show that mixing with material from predicted yields of massive,
rotating AGB stars at low metallicity considerably improves the fit. Based on a
solar ratio of heavy- to light-s elements -- at odds with model predictions for
the i-process -- and a missing clear residual pattern with respect to other
stars with claimed contributions from this process, we refute (strong)
contributions from such astrophysical sites providing intermediate neutron
densities. Finally, nuclear cosmochronology is used to tie our detection of the
radioactive element Th to an age estimate for HD 20 of $11.0\pm3.8$ Gyr.
[abridged]
