Appointees do have to be approved by the Senate, but we’ve already seen that the republicans are perfectly happy to rubber stamp anyone who will favor republican policies. I don’t know if the president could appoint himself, but I’d bet a republican-controlled senate would be happy to confirm him even if some law theoretically disallows it. The president cannot himself remove the justices through any mechanism of law (as if he cares about that), but justices can be removed by Congress via impeachment. I am not a lawyer, but I’m thinking a sufficiently corrupt congress/senate could make it happen.

It’s depressing how much of our government and legal system relied on the idea that at least most people would act in good faith.