Would the court also need to carefully consider and rule on whether arresting or murdering a disagreeing judge is an "official act" by the President?

Probably not. Arresting disagreeing judges would be a violation of due process, as is murdering US citizens without a trial.

At least that was the tentative conclusion last time this was brought up: https://www.theguardian.com/commentisfree/2013/feb/22/obama-...

It might be a violation of the law and clearly illegal, but that does not mean it is not an official act for which the president is immune.

I disagree, since a good many people seem ready to accept that Trump trying to overturn the results of a free and fair election (which in my book is pretty much on par with murdering political rivals since the point of murdering a rival is so that they don't get elected), is an "official duty".