We describe how color superfluidity is modified in the complex order parameter with no momentum dependence and by inert unpaired fermions representing a non-superfluid component. In the latter case, just a crossover between a Bardeen-Cooper-Schrieffer and a Bose-Einstein-Condensation superfluid occurs. Furthermore, we analyze the order parameter tensor in a total pseudo-spin basis, investigate its momentum dependence in the singlet, triplet and quintet sectors, and compare the results with the simpler case of spin-1/2 fermions in the presence of spin-flip and spin-orbit fields, where only singlet and triplet channels arise. Finally, we analyze in detail spectroscopic properties of color superfluids in the presence of color-flip and color-orbit fields, such as the quasiparticle excitation spectrum, momentum distribution, and density of states to help characterize all the encountered topological quantum phases, which can be realized in fermionic isotopes of Lithium, Potassium and Ytterbium atoms with three internal states trapped.