You are so confused. If necessary and proper means what Will says it does, which was explicitly rejected by the framers, then of course Congress has the power to micromanage all aspects of the executive. That's the point! As for a check on the president, go back to the Constitution -- Congress can defund the program, it can defund the war, it can impeach ... it has much power. Just not the power to run the executive branch. This isn't a mobocracy or parliamentary system.
No, Congress can't tell the executive whom to arrest or where to position troops or which lines to surveil. Those are executive decisions. It can, however, limit the scope of action of his agencies to what Congress decides is necessary for him to do his job. Congress gave him these agencies, and Congress can limit what it gives to him.
And the "checks" that you mention are utterly unrealistic. Making a choice between not having the ability to defend ourselves at all and living with presidential abuses of power is not a "check"; it's a joke. And talking about impeachment merely begs the question. Impeachment is for violations of the law, but if Congress can't pass a law regulating him, there's no law for him to violate.