I have no doubt if such a case was brought to them they'd just rule impeachment a "political question" and remove any jurisdiction over it.
They already did, in 1993's Nixon v. United States.
Yes, it does seem that addressed it.
but I can imagine at least one hypothetical where they would have to take it up again: If someone was impeached for something that was a part of their religion, due to the "no religious Test" clause.
Eh, that'd arguably still constitute a nonjusticiable political question, since the Religious Test clause only applies to qualifications for office & conviction in & of itself only
removes the impeached official from office as opposed to disqualifying them. Now, if the Senate were to then go ahead & disqualify said individual from holding office again in the future as well, then that'd potentially make for an interesting case, but even then, I don't know if the Court would be all that inclined to take it up.