  A long sought after goal using chemical abundance patterns derived from
metal-poor stars is to understand the Galactic chemical evolution (GCE) and to
pin down the nature of the first stars (Pop III). Here, we use a sample of 14
metal-poor stars observed with the high-resolution spectrograph PEPSI at the
LBT to derive abundances of 32 elements (34 including limits). We present
well-sampled abundance patterns for all stars obtained using local
thermodynamic equilibrium (LTE) radiative transfer codes and 1D hydrostatic
model atmospheres. It is currently well known that the assumptions of 1D and
LTE may hide several issues, thereby introducing biases in our interpretation
as to the nature of the first stars and the GCE. Hence, we use non-LTE (NLTE)
and correct the abundances using 3D model atmospheres to present a physically
more reliable pattern. In order to infer the nature of the first stars, we
compare unevolved, cool stars, enriched by a single event (`mono-enriched'),
with a set of yield predictions to pin down the mass and energy of the Pop III
progenitor. To date, only few bona fide second generation mono-enriched stars
are known. A simple x^2-fit may bias our inferred mass and energy just as much
as the simple 1D LTE abundance pattern, and we thus carried out our study with
an improved fitting technique considering dilution and mixing. Our sample
presents Carbon Enhanced Metal-Poor (CEMP) stars, some of which are promising
true second generation (mono-enriched) stars. The unevolved, dwarf BD+09_2190
shows a mono-enriched signature which, combined with kinematical data,
indicates that it moves in the outer halo and likely has been accreted onto the
Milky Way early on. The Pop III progenitor was likely of 25.5M and 0.6 10^51erg
(foe)/19.2M and 1.5foe in LTE/NLTE. Finally, we explore the predominant donor
and formation site of the rapid and slow neutron-capture elements. Abridged
