  We consistently include the effect of massive neutrinos in the thermal
Sunyaev Zeldovich (SZ) power spectrum and cluster counts analyses, highlighting
subtle dependencies on the total neutrino mass and data combination. In
particular, we find that using the transfer functions for Cold Dark Matter
(CDM) + baryons in the computation of the halo mass function, instead of the
transfer functions including neutrino perturbations, as prescribed in recent
work, yields a $\approx$ 0.25\% downward shift of the $\sigma_8$ constraint
from tSZ power spectrum data, with a fiducial neutrino mass $\Sigma m_\nu=0.06$
eV. In $\Lambda$CDM, with an X-ray mass bias corresponding to the expected
hydrostatic mass bias, i.e., $(1-b)\simeq0.8$, our constraints from Planck SZ
data are consistent with the latest results from SPT, DES-Y1 and
KiDS+VIKING-450. In $\nu\Lambda$CDM, our joint analyses of Planck SZ with
Planck 2015 primary CMB yield a small improvement on the total neutrino mass
bound compared to the Planck 2015 primary CMB constraint, as well as
$(1-b)=0.64\pm0.04$~(68\%~CL). For forecasts, we find that competitive neutrino
mass measurements using cosmic variance limited SZ power spectrum require
masking the heaviest clusters and probing the small-scale SZ power spectrum up
to $\ell_\mathrm{max}\approx10^4$. Although this is challenging, we find that
SZ power spectrum can realistically be used to tightly constrain intra-cluster
medium properties: we forecast a 2\% determination of the X-ray mass bias by
combining CMB-S4 and our mock SZ power spectrum with $\ell_\mathrm{max}=10^3$.
