Has a diplomat or member of an embassy staff ever committed murder? What happens in this instance? Does their immunity remain intact?

Diplomatic immunity does not grant someone a license for meyham. It DOES prevent them from getting minor things such as traffic and parking tickets.

The level of immunity depends on the agreement with the host and parent country. In a case such as murder, the host will allow the parent country to prosecute the diplomat accordingly.

Almost invariably, they offender will have their credentials revoked and they will be sent back to their home country. There have been cases where the parent country has allowed the host country to prosecute.

In a case like this, the US State Depatment would work with the leaders of their nation to have their status removed to allow them to be detained for trial.

But without permission though the State Department they can not be held.