Measurements of open charm production cross sections in deep-inelastic ep scattering at HERA from the H1 and ZEUS Collaborations are combined. Reduced cross sections σ _red ^cc̄ for charm production are obtained in the kinematic range of photon virtuality 2. 5≤Q ² ≤2000 GeV ² and Bjorken scaling variable 3{dot operator}10 ^-5 ≤x≤5{dot operator}10 ^-2 . The combination method accounts for the correlations of the systematic uncertainties among the different data sets. The combined charm data together with the combined inclusive deep-inelastic scattering cross sections from HERA are used as input for a detailed NLO QCD analysis to study the influence of different heavy flavour schemes on the parton distribution functions. The optimal values of the charm mass as a parameter in these different schemes are obtained. The implications on the NLO predictions for W ^± and Z production cross sections at the LHC are investigated. Using the fixed flavour number scheme, the running mass of the charm quark is determined.