“Was the Roman Empire better or worse than the Roman Republic from a libertarian point of view?”
This is a difficult question to answer, since each period spans 500 years. There were ups and downs in each. Generally speaking, the early republic and early empire are less bad than the later republic and later empire in terms of taxation, wars, etc. On the other hand, common people gradually gained more liberties between the founding of the republic and the early third century B.C. as a result of the Struggle of the Orders. So it’s a mixed bag.
“Does Hoppe’s theory of monarchy and democracy apply to Roman history?”
The difference between the republic and empire is one of aristocracy (Senate) vs. monarchy, so the parallel is not exact. The structures of both republic and empire provided incentives to implement policies sensible over the long run.
“How much aggression did the Roman government commit against ordinary people during the various stages of its history?”
This is a very broad question. Are you trying to compare the Roman government to some other State?