High penalties can incentivize to commit further crimes, at least. An extreme example might be capital punishment for robbery, which I'd expect (but haven't seen statistics, or don't remember) would increase the rate of murder committed during robberies.
Yes! A good example is three-strikes laws, where a misdemeanor can get you a life sentence, so some criminals are highly incentivized to aggressively fight an additional arrest, with very little marginal incentive not to commit murder to do so.
From a 2015 study[1]:
"Three-strikes laws were associated with a 33% increase in the risk of fatal assaults on LEOs."
