  Iron plays a crucial role in studies of late-type stars. In their
atmospheres, Fe I is the minority species and its lines are subject to the
departures from LTE. In contrast, one believes that LTE is a realistic
approximation for Fe II lines. The main source of the uncertainties in the
non-LTE (NLTE) calculations for cool atmospheres is a treatment of inelastic
collisions with hydrogen atoms. We investigate the effect of Fe I + H I and Fe
II + H I collisions and their different treatment on the Fe I/Fe II ionisation
equilibrium and Fe abundance determinations for Galactic halo benchmark stars
HD84937, HD122563, and HD140283 and a sample of 38 very metal-poor giants in
the dwarf galaxies with well known distances. We perform the NLTE calculations
for Fe I-II with using quantum-mechanical (QM) rate coefficients for collisions
with H I from Barklem (2018, B18), Yakovleva, Belyaev, and Kraemer (2018,
YBK18), and Yakovleva, Belyaev, and Kraemer (2019). We find that collisions
with H I serve as efficient thermalisation processes for Fe II and the NLTE
abundance corrections for Fe II lines do not exceed 0.02 dex at [Fe/H] > -3 and
reach +0.06~dex at [Fe/H] ~ -4. For given star, the B18 and YBK18 treatments of
Fe I + H I collisions lead to similar average NLTE abundances from Fe I lines,
although there exist discrepancies in the NLTE corrections for individual
lines. With using QM collisional data and the Gaia based surface gravity, we
obtain consistent abundances from Fe I and Fe II for a red giant HD122563. For
HD84937 and HD140283, we study the Fe lines in the visible and the UV
(1968-2990 A) range. For both Fe I and Fe II, abundances from the visible and
UV lines are consistent. The abundances from Fe I and Fe II agree within 0.10
and 0.13 dex in the YBK18 and B18 cases. The Fe I/Fe II ionisation equilibrium
is achieved for each [Fe/H] > -3.5 star of our dwarf galaxy sample.
