If, for example, a husband finds his wife naked on a bed with another man but does not actually witness them in the act of coitus, what is the shari’ah ruling if he, in his disturbed state, kills them? Such killings are not uncommon in Muslim societies. What is the shari’ah punishment for each of the individuals described above. What for example is the punishment for rape in places where punishments – hadd – decreed by an Islamic state do not exist?

1. The husband in your question is not permitted to kill any of the people whom you mentioned. The Shari’ah gives the choice to such a man to divorce his wife, but gives him no right to kill her.
2. Crimes of passion are not observed in Muslim societies any more frequently than they are in non-Muslim societies.
3. Shari’ah punishments are dependent on circumstances.
The lady who has committed the sin of being naked with a man who is not her spouse must repent with sincerity and ask Allah for forgiveness.

In Islamic states where a Just Ruler is the Head of State, there are hudud punishments for some sins. You however are talking about lands in which hadd is not practised. Punishments for murder and rape are determined by the country in which they are committed.