Zero-energy flat bands within the superconducting gap can give rise to competing ordered phases. We investigate such phases in topological superconductors based on the magnetic adatom platform hosting a flat band of Majorana edge states. Our self-consistent calculations of the superconducting order parameter show the emergence of both a pair density wave with edge-localized amplitude modulations, often a bond wave order, and a phase crystal characterized by longer-wavelength edge-localized phase modulations. Both these states lower the free energy by gapping out the Majorana flat band, but use different mechanisms tied to the underlying topology. In fact, at zero temperature the uniform superconducting solution with Majorana flat band never survives. Instead, a pair density wave appears when sufficient Majorana modes exist with oppositely signed topological winding numbers, while a phase crystal appears in regions of the phase diagram where one non-trivial winding number is heavily dominating. A crossover region connects these two states with modulations in both amplitude and phase. At finite temperatures, the pair density wave survives up to around 80% of the bulk superconducting transition temperature, while the phase crystal only appears at lower temperatures and the crossover region is also strongly suppressed. Our findings establish the ubiquity of emergent nonuniform superconducting phases and their temperature-dependent behavior in topological superconductors.