Question: Pence kills Trump to become President. Would he be immune?

[hlthe2b]

9. Because until JFK, there was not an official mechanism to name the line of succession,

the 25th amendment was passed. Technically, this is why from Tyler to LBJ, they've rushed to take the oath of office, because they were sort of in limbo land. The 25th amendment made it clear that if the President is incapacitated (or dead), the VP or whoever is next in line of succession becomes the President pending taking the official oath.

https://constitutioncenter.org/blog/how-jfks-assassination-led-to-a-constitutional-amendment

In your scenario, the swearing in/oath could be denied to a VP with the Supreme Court undoubtedly having to rule on the VP being legally eligible/ineligible to assume the Presidency. If there was a obvious cloud over the VP, the cabinet could likely invoke the 25th temporarily against him/her to buy time.