  The Milky Way is a mosaic of stars from different origins. In particular,
metal-poor accreted star candidates offer a unique opportunity to better
understand the accretion history of the Milky Way. In this work, we aim to
explore the assembly history of the Milky Way by investigating accreted stars
in terms of their ages, dynamical properties, and chemical abundances. We also
aim to better characterize the impact of incorporating asteroseismic
information on age and chemical abundance calculations of metal-poor accreted
stars for which TESS data is available. In this study, we conducted an in-depth
examination of 30 metal-poor accreted star candidates, using TESS and Gaia
data, as well as MIKE spectra. We find satisfactory agreement between seismic
and predicted/spectroscopic surface gravity (log g) values, demonstrating the
reliability of spectroscopic data from our methodology. We found that while age
determination is highly dependent on the log g and asteroseismic information
used, the overall chemical abundance distributions are similar for different
log g. However, we found that calcium (Ca) abundances are more sensitive to the
adopted log g. Our study reveals that the majority of our stars have properties
compatible to those reported for the Gaia-Sausage-Enceladus, with a minority of
stars that might be associated to Splash. We found an age distribution with a
median of 11.3 Gyr with lower and upper uncertainties of 4.1 and 1.3 Gyr
respectively when including asteroseismic information. As regarding some key
chemical signatures we note that these stars are metal-poor ([Fe/H]) < -0.8),
alpha-rich ([alpha]/Fe] > 0.2), copper-poor ([Cu/Fe] < 0 ) and with chemical
abundances typical of accreted stars. These findings illustrate the importance
of multi-dimensional analyses in unraveling the complex accretion history of
the Milky Way.
