Detailed investigations of Ni substituted Fe_0.94Ni_0.007Te_0.66Se_0.34 and unsubstituted Fe_0.99Te_0.66Se_0.34 crystals were performed at ambient and under hydrostatic pressure in order to understand complex relationship between the structure, magnetism, and superconductivity in iron selenides. The investigations aimed at determining structural and superconducting state properties and studying their evolution under pressure up to 11 kbar. Comparison of Fe_0.99Te_0.66Se_0.34, a material with much less developed phase separation, with FeTe_0.5Se_0.5, a material exhibiting well pronounced nanoscale phase separation, was also performed. Under ambient pressure the weakening of superconducting state properties was observed in Fe_0.94Ni_0.007Te_0.66Se_0.34 crystal, with disorder introduced by Ni substitution, as compared with those in Fe_0.99Te_0.66Se_0.34. For Fe_0.94Ni_0.007Te_0.66Se_0.34, the X-ray diffraction studies have revealed a degradation of crystal quality under applied elevated pressure. Superconducting state properties of single phase Fe_0.99Te_0.66Se_0.34 crystal, such as upper and lower critical fields, were found to be poorer, at both ambient and hydrostatic pressure, than those observed for FeTe_0.5Se_0.5 crystals exhibiting pronounced nanoscale phase separation. Comprehensive studies of impact of pressure on crystal structure and on superconducting state properties confirm that enhancement of superconductivity correlates with appearance of mosaicity under pressure. The above observation leads to expectation of pressure induced increase of inhomogeneity, leading to enhancement of superconducting properties in other sulpho-iron seleno-tellurides of anti-PbO-type structure.