  This work presents a large consistent study of molybdenum (Mo) and ruthenium
(Ru) abundances in the Milky Way. These two elements are important
nucleosynthetic diagnostics. In our sample of 71 Galactic metal-poor field
stars, we detect Ru and/or Mo in 51 of these (59 including upper limits). The
sample consists of high-resolution, high signal-to-noise spectra covering both
dwarfs and giants from [Fe/H]=-0.63 down to -3.16. Thus we provide information
on the behaviour of Mo I and Ru I at higher and lower metallicity than is
currently known. We find a wide spread in the Mo and Ru abundances, which is
typical of heavy elements. This indicates that several formation processes, in
addition to high entropy winds, can be responsible for the formation of Mo and
Ru. The formation processes are traced by comparing Mo and Ru to elements (Sr,
Zr, Pd, Ag, Ba, and Eu) with known formation processes. We find contributions
from different formation channels, namely p-, slow (s-), and rapid (r-)
neutron-capture processes. Molybdenum is a highly convolved element that
receives contributions from several processes, whereas Ru is mainly formed by
the weak r-process as is silver. We also compare our absolute elemental stellar
abundances to relative isotopic abundances of presolar grains extracted from
meteorites. Their isotopic abundances can be directly linked to the formation
process (e.g. r-only isotopes) providing a unique comparison between
observationally derived abundances and the nuclear formation process. The
comparison to abundances in presolar grains shows that the r-/s-process ratios
from the presolar grains match the total elemental chemical composition derived
from metal-poor halo stars with [Fe/H]~ -1.5 to -1.1 dex. This indicates that
both grains and stars around and above [Fe/H]=-1.5 are equally (well) mixed and
therefore do not support a heterogeneous presolar nebula... Abridged.
