In this work, magnetization dynamics is studied at low temperatures in a hybrid system that consists of a thin epitaxial magnetic film coupled with a superconducting planar microwave waveguide. The resonance spectrum was observed over a wide magnetic field range, including low fields below the saturation magnetization and both polarities. Analysis of the spectrum via a developed fitting routine allowed for the derivation of all magnetic parameters of the film at cryogenic temperatures, the detection of waveguide-induced uniaxial magnetic anisotropies of the first and the second order, and the uncovering of a minor misalignment of magnetic field. A substantial influence of the superconducting critical state on resonance spectrum is observed and discussed.