Recent STM experiments show that by exposing h-BN/Rh(111) nanomesh to water or atomic hydrogen interesting phenomena can be observed. We investigated by Density Functional Theory (DFT) the structure of bare nanomesh as well as in the presence of water clusters and atomic hydrogen. Our simulations allow the correct interpretation of the observed modifications of the STM topography under different tested conditions. For example, we could determine that the frequently observed three protrusions within the pore appearing in STM images obtained after dosing small amounts of water, are most likely determined by water hexamers. We also could confirm that the flattening of the h-BN overlayer after dosing atomic hydrogen is determined by the intercalation of the latter between BN and metal, which prevents the effective binding between N and Rh.