Specifically, I'm interested in punishments. Could the owner have a slave killed as punishment for any perceived wrongdoing? Was it possible for the owner to sentence the slave to some gruesome form of death (skinning, imapling), if the owner had sadistic inclinations?
The slave owner had the same right over his slave as he did a piece of his property, i.e any inanimate object in his house. The very existence of slaves was abhorrent, however slaves were essentially business commodities and they were not cheap. Therefore, fatal punishments and tortures were not in the best interests of the slave owner.
Edit: Yes, the slave owner could do what he pleased with his slave, but killing them was not necessarily a good move on their part.