OK, would you please give me a scenario or two where an official act of the president would be criminal?

Again, it's the distinction you provided. If the President offered to grant a pardon in exchange for the murdering of a political rival, the actus rea of the crime would be the conspiracy to commit murder. The President is immune from being prosecuted for granting a pardon, but he isn't immune from entering into an agreement for a murder to be committed. Because arranging for someone to be murdered isn't an official act of the President - it's not something he's legally allowed to do.

This isn't some far out, crazy, completely novel concept. U.S. Congressmen enjoy absolute immunity - civil and criminal - for their votes and speech in their respective Congressional chambers. That's not under dispute, because unlike the Presidential case the Constitution explicitly grants them that immunity in the Speech and Debate Clause. So as you might expect, the courts have had to deal with the scope of that immunity in the context of allegations that Congressmen were bribed to vote or speak in a certain way:

https://supreme.justia.com/cases/federal/us/383/16...

It doesn't shield them from criminal charges absolutely. If a Congresscritter agreed to give a speech or take a vote in exchange for a hit on a political rival, they'd still be prosecutable for conspiracy to commit murder. It's just that the speech or vote cannot on its own be the "actus rea" (the unlawful act) that supports the crime. The elements of the crime have to be met with things other than the vote or speech.

Again, many countries have this sort of criminal immunity for legislators - either for when they're doing the legislative things (like in the U.S., and in virtually every Westminster parliamentary system), and sometimes more broadly (as in France or Germany, where legislators enjoy not just immunity in their legislative functions but in other conduct as well). These countries have not been wracked by crime waves of legislators assassinating their election rivals in exchange for votes...