Well, one big reason that drives slaine is jealousy imho. Most of what he did was driven by a mixed feeling of helping/saving his princess and jealousy of inaho. He saw how the princess was clinging to him, so he shot him. He heard bout remembering his time on earth with inaho (remember the scene where he wanted to bringe her flowers and then leave when he hear her remembering bout inaho?, leaving the flowers on the ground). I think becoming a count was in his plans, that is why he didnt kill sazbaum right away, but killed him the moment he got nominated has heir. Another big reason its that he truely want to get out of the cast sytem that was estabilish on mars/vers, but to do that he need resource from earth, and power to command the knights (i think the comment about he not being a vers citizen its because he doesnt reconize himself into the cast sytem and want to create a new system). Aldnoah activations right was given by the princess, she can bestows the rights since she has royal blood, so he doesnt need her presence to activate it, as inaho doesnt need it its like an aquired skill, if you want.