We can not prosecute or arrest those with diplomatic immunity.
I do not think this EO gives INTERPOL ‘Diplomatic Immunity’. It is part of agreement contained within international law in the Vienna Convention on Diplomatic Relations (1961). The Convention does not cover the personnel of international organizations. Specific and important within the Convention. Those personnel have their privileges are decided upon on a case-by-case basis, which usually rely on the treaties and are found in the treaties founding such organizations.
No I believe you are wrong on this count. I think the EO just gave them relief from search and seizure of their organizational property/data.
I believe I'm right unless the article has it wrong. To quote:
This international police force ...will be unrestrained by the U.S. Constitution and American law while it operates in the United States and affects both Americans and American interests outside the United States.That seems quite unambiguous to me.