We report muon spin relaxation and rotation ($mu$SR) measurements on hydrothermally-grown single crystals of the tetragonal superconductor~FeS, which help to clarify the controversial magnetic state and superconducting gap symmetry of this compound. $mu$SR time spectra were obtained from 280~K down to 0.025~K in zero field (ZF) and applied fields up to 20 mT. In ZF the observed loss of initial asymmetry (signal amplitude) and increase of depolarization rate~$Lambda_mathrm{ZF}$ below 10~K indicate the onset of static magnetism, which coexists with superconductivity below $T_c$. Transverse-field $mu$SR yields a muon depolarization rate $sigma_mathrm{sc} propto lambda_{ab}^{-2}$ that clearly shows a linear dependence at low temperature, consistent with nodal superconductivity. The $s{+}d$-wave model gives the best fit to the observed temperature and field dependencies. The normalized superfluid densities versus normalized temperature for different fields collapse onto the same curve, indicating the superconducting gap structure is independent of field. The $T=0$ in-plane penetration depth $lambda_{ab}$(0) = 198(3) nm.
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