1.a I suppose the nm units of the table are nuclear magnetons, so we can rewrite the expression of the g-factor to be: g=mu*hbar/I, where the mu is in nuclear magnetons. I then doubt if the hbar is still supposed to be here, since on this wikipedia (https://en.wikipedia.org/wiki/Nuclear_magnetic_moment#cite_note-Bruker-11) page for example, the just say g=mu/I (also with mu in nm). I will do it this way, since i also think it gives a better understanding of the meaning of the g-factor. So for the ground state we have: g=-0.5940*2=-1.188 and for the excited state we get: g=(-0.766*2)/5=-0.3064 both are supposed to be dimensionless.
1.b The electron has a spin of 1/2, so the g-factor must be 2