Differential thermal analysis (DTA), at argon pressures up to 1.55 GPa, has been performed in order to determine the melting curves of mercury chalcogenides and their alloys with iron (diluted magnetic semiconductors). A three-zone furnace with the option of a programmable temperature gradient was constructed, which can be installed inside a gas pressure chamber. Experiments were carried out under gas pressures of argon or nitrogen up to 1.55 GPa in a gas chamber of 30 mm internal diameter; the temperature range used was 25-900 degrees C. The authors have found that the melting point for both HgTe and Hg_1-xFe_xTe decreases with pressure and is lower for iron-doping materials. The slope of the melting curve is close to the value of -46 degrees C GPa^-1 evaluated by Jayaraman et al. However, for HgTe the experiments did not confirm the phase transition from zinc blende to cinnabar (B3 to B9) with the change of the liquidus slope (from -46 to 115 degrees C GPa^-1) reported by Jayaraman et al at 1.2 GPa. On the basis of DTA results single crystals of HgTe and Hg_1-xFe_xTe have been grown under gas pressures up to 1.5 GPa using a gradient freeze method. The crystals were characterized by X-ray diffraction, EDX and electronic transport measurements.