This thesis presents the investigation of the two-body scattering properties of cold atoms in sodium and lithium-sodium mixtures and their effects on the many body dynamics. Since both species are alkali atoms, the combined spin of both unpaired electrons can be either zero or one, providing two different scattering channels. The coupling of bound molecular states in these channels with the free atoms asymptote gives rise to the rich field of Feshbach resonance physics, where the interaction between the particles can be controlled as an easily accessible experimental parameter. We have investigated the Feshbach spectrum in the bosonic LiNa mixture and could confirm predictions based on LiNa measurements, with a shift of the predicted spectrum by about 50 G. Also, the prospects of interaction tuning via Feshbach resonances were examined. The difference of the scattering lengths of the electronic potentials also causes a coupling of atomic collisional channels, which can enable a spin exchange between the atoms. In this thesis, spin exchange processes have been studied in coherent oscillations in a thermal gas and a Bose-Einstein condensate of sodium, as well as the evolution of this spinor gas into its ground state. Preliminary studies of the heteronuclear spin exchange process in both the bosonic LiNa and in the fermionic-bosonic mixture LiNa are presented as well.