We focus on an in-depth study of the forced dynamics of a ferromagnetic single-domain uniaxial nanoparticle placed in a viscous fluid and driven by an external rotating magnetic field. The process of conversion of magnetic and mechanical energies into heat is a physical basis for magnetic fluid hyperthermia that is very promising for cancer treatment. The dynamical approximation allows us to establish the limits of the heating rate and understand the logic of selection of the system parameters to optimize the therapy. Based on the developed analytical and numerical tools, we analyze from a single viewpoint the synchronous and asynchronous rotation of the nanoparticle or/and its magnetization in the following three cases. For the beginning, we actualize the features of the internal magnetic dynamics, when the nanoparticle body is supposed to be fixed. Then, we study the rotation of the whole nanoparticle, when its magnetization is supposed to be locked to the crystal lattice. And, finally, we realize the analysis of the coupled motion, when the internal magnetic dynamics is performed in the rotated nanoparticle body. In all these cases, we describe analytically the uniform mode, or synchronous rotation along with an external field, while the nonuniform mode, or asynchronous rotation, is investigated numerically.