The mayor of DC has to request the National Guard be brought in. The same is true for the City of Portland, for example.
The DC National Guard is under the command of the President. The President has delegated that to the Secretary of Defense, who delegated to the Secretary of the Army. This may be the case prior to President Trump; I didn’t research that far back. So the Secretary of the Army is who approved this build-up.
The state National Guard who have been sent to DC fall under the command of the DC National Guard. That means they’re under the direct command of the President/Secretary of Defense/Secretary of the Army.
Correct
This was the chain of command even before President Trump.