  We derive the formal Ward identities relating pseudoscalar susceptibilities
and quark condensates in three-flavor QCD, including consistently the
$\eta$-$\eta'$ sector and the $U_A(1)$ anomaly. These identities are verified
in the low-energy realization provided by ChPT, both in the standard $SU(3)$
framework for the octet case and combining the use of the $U(3)$ framework and
the large-$N_c$ expansion of QCD to account properly for the nonet sector and
anomalous contributions. The analysis is performed including finite temperature
corrections as well as the calculation of $U(3)$ quark condensates and all
pseudoscalar susceptibilities, which together with the full set of Ward
identities, are new results of this work. Finally, the Ward identities are used
to derive scaling relations for pseudoscalar masses, which explain the behavior
with temperature of lattice screening masses near chiral symmetry restoration.
