  Extremely metal-poor stars provide us with indirect information on the first
generations of massive stars. The TOPoS survey has been designed to increase
the census of these stars and to provide a chemical inventory that is as
detailed as possible. Seven of the most iron-poor stars have been observed with
the UVES spectrograph at the ESO VLT Kueyen 8.2m telescope to refine their
chemical composition. We analysed the spectra based on 1D LTE model
atmospheres, but also used 3D hydrodynamical simulations of stellar
atmospheres. We measured carbon in six of the seven stars: all are
carbon-enhanced and belong to the low-carbon band, defined in the TOPoS II
paper. We measured lithium (A(Li)=1.9) in the most iron-poor star (SDSS
J1035+0641, [Fe/H] < -5.2 ). We were also able to measure Li in three stars at
[Fe/H]~ -4.0, two of which lie on the Spite plateau. We confirm that SDSS
J1349+1407 is extremely rich in Mg, but not in Ca. It is also very rich in Na.
Several of our stars are characterised by low alpha-to-iron ratios. The lack of
high-carbon band stars at low metallicity can be understood in terms of
evolutionary timescales of binary systems. The detection of Li in SDSS
J1035+0641 places a strong constraint on theories that aim at solving the
cosmological lithium problem. The Li abundance of the two warmer stars at
[Fe/H]~ -4.0 places them on the Spite plateau, while the third, cooler star,
lies below. We argue that this suggests that the temperature at which Li
depletion begins increases with decreasing [Fe/H]. SDSS J1349+1407 may belong
to a class of Mg-rich EMP stars. We cannot assess if there is a scatter in
alpha-to-iron ratios among the EMP stars or if there are several discrete
populations. However, the existence of stars with low alpha-to-iron ratios is
supported by our observations.
