Measurements of open beauty and charm production cross sections in deep inelastic scattering (DIS) at HERA by the H1 and ZEUS Collaborations are combined. Reduced cross sections for beauty and charm production are obtained in $ep$ collisions at a centre-of-mass energy $\sqrt{s}=319\,\text{GeV}$ in a kinematic range of the photon virtuality $2.5<Q^2<2000\,\text{GeV}^2$ and the Bjorken scaling variable $3\times10^{-5}<x<5\times10^{-2}$. The combination method accounts for the correlations of the systematic uncertainties among the different data sets. The combined data are compared to perturbative QCD predictions at next-to-leading order (NLO). The running charm and beauty quark masses are extracted. Furthermore, open charm production is studied in diffractive DIS at $5<Q^2<100\,\text{GeV}^{2}$, based on data recorded by the H1 experiment. The event topology is given by $ep\to eXY$, where the system $X$, containing at least one $D^{*}(2010)$ meson, is separated from a leading momentum low-mass proton-dissociative system $Y$ by a large rapidity gap. The measured cross sections are compared with NLO QCD predictions based on previously determined diffractive parton densities of the proton.