Understanding of physicochemical interactions of proteins and other biologically significant molecules with shungite nanocarbon (ShC), a graphene family nanomaterial, is required to provide biosafety in various fields of its application including biomedicine. Dynamic characteristics of potential bio-nano interface, characteristics of interaction with the solvent (hydration) carry important information about the types of arising bonds and interactions, the interaction of ligand transfer among them, as well as about the properties of the corresponding bio-nano hybrid forms. The dynamic state of the interface (surface) of carbon nanoclusters in ShC dispersions and protein (bovine serum albumin, BSA) and other biologically significant molecules and ions (sucrose, urea, NaCl, HCl, NaOH) that can affect hydration have been studied using electron spin resonance (ESR) of spin probe based on stearic fatty acid (FA) molecule. A transfer of spin probe (FA) from protein to nanocarbon and vice versa in a mixed dispersion of ShC and BSA has been shown to occur depending on their concentration ratio. Nanoparticle protein corona is probably involved in the transfer. The effect has been observed at ShC concentration an order of magnitude lower than that of protein. This signifies the possibility to influence FA binding and transport by serum albumin using ShC dispersion. This effect can be regulated by additional solutes, as has been observed in the case of sucrose. Nonlinearities of Arrhenius dependences of ESR spin probe spectrum parameters in mixed ShC dispersions may indicate the phase transition as in polymer solutions.