It is enumerated under the legislative branch, not the executive, not the judiciary. The Supreme Court ruled that it could not be suspended without an act of Congress. The Supreme Court was ignored.
Congress did not approve it upon returning to session in 1861. It was not approved by Congress until 1863.
The entire court has never taken the matter up, so they have never ruled one way or the other.
Not true. The Court has never said who can suspend it.