On the declaration of war, Senator Biden has my back:

M: (Inaudible) Talbot(?). Senator, thank you for this broad gauged approach to the problems we face. My question is this, do you foresee the need or the expectation of a Congressional declaration of war, which the Constitution calls for, and if so, against whom? (Scattered Laughter)

JB: The answer is yes, and we did it. I happen to be a professor of Constitutional law. I'm the guy that drafted the Use of Force proposal that we passed. It was in conflict between the President and the House. I was the guy who finally drafted what we did pass. Under the Constitution, there is simply no distinction ... Louis Fisher(?) and others can tell you, there is no distinction between a formal declaration of war, and an authorization of use of force. There is none for Constitutional purposes. None whatsoever. And we defined in that Use of Force Act that we passed, what ... against whom we were moving, and what authority was granted to the President.

And from the AUMF 2001:

...the President is authorized to use all necessary and appropriate force against those nations, organizations, or persons he determines planned, authorized, committed, or aided the terrorist attacks that occurred on September 11, 2001, or harbored such organizations or persons...

From the AUMF 2002 (PDF), which the good senator references:

The President is authorized to use the
Armed Forces of the United States as he determines to be necessary
and appropriate in order to--
(1) defend the national security of the United States against
the continuing threat posed by Iraq; and
(2) enforce all relevant United Nations Security Council
resolutions regarding Iraq.

And Justice O'Connor wrote extensively about the issue of indefinite detention in Hamdi v. Rumsfeld. I guess you couldn't be bothered to read it, so I'll just quote it here, too.

[W]e understand Congress' grant of authority for the use of "necessary and appropriate force" to include the authority to detain for the duration of the relevant conflict, and our understanding is based on longstanding law-of-war principles. If the practical circumstances of a given conflict are entirely unlike those of the conflicts that informed the development of the law of war, that understanding may unravel. But that is not the situation we face as of this date. Active combat operations against Taliban fighters apparently are ongoing in Afghanistan....The United States may detain, for the duration of these hostilities, individuals legitimately determined to be Taliban combatants who "engaged in an armed conflict against the United States." If the record establishes that United States troops are still involved in active combat in Afghanistan, those detentions are part of the exercise of "necessary and appropriate force," and therefore are authorized by the AUMF.