Within our own nation, in time of emergency or insurrection, the Congress does not have to declare war. But armed conflict with foreign powers is not within our own nation.
Is the use of military force constitutionally restricted to declared wars? No.
You're right. It can be used within our own country in times of emergency.
Is Congress constitutionally obligated to declare war each and everytime the need to engage US Armed Forces arises? No.
Oh? Congress can declare war generally and leave it to the executive to decide when? That is tantamount to violation to the separation of powers. The separation of powers doctrine is about keeping a single head from wielding all powers of state.
It either keeps all powers separated into the various branches or it doesn't. There is no part here and part there. If one power can be legitimately transfered, then they all can by implication. If one branch's power is de facto in the hands of another, it doesn't matter if in some labored way it was made de jure, it actually does what the framers of our constitution preached against and materially (not just philosophically) brings about the dangers of a totalitarian form of administration.
I was taught this in every civics class I had in school many years ago. Weren't you?
Is the definition of "war" limited to "...armed conflict with another nation..." as stated by you? No, as proven by The Civil War.
The war was not a "civil war". The south didn't attempt to attack the national government and take it over; they withdrew from it and formed a new nation with the consent of the people and electorate. That it was two nations fighting, no matter how the people on both sides thought about one another, made it not an internal emergency.
Regardless of the rhetoric, the fact is, the south left the union and formed a new nation with a constitution. They were conquered by the North in a war. Their nation was declared "illegal" only after they were conquered
Can the definition of "war" include armed conflict with multi-national paramilitary organizations such as terrorists? Yes.
We're talking about Iraq. Iraq is a aggregate people operating as a sovereign nation, only it has a very dangerous leader. Links to terrorism are only one of the list of national security reasons given by the president. I think Saddam is a threat to us. Let's kick his ass. But let's do it by the book lest the book cease to have meaning.
Can Congress grant authorization to use force to the Commander In Chief pending international developments? Yes, under the War Powers Act.
"Act" means legislation. Which would mean Congress granted themselves the power to transfer their power to declare war to the executive, or "grant authorization to use force to the Commander In Chief pending international developments".
Is the War Powers Act constitutional? Yes, it was penned under the authorization granted to Congress by the U.S. Constitution, Article I, Section 8, Clause 18.
" 18. To make all Laws which shall be necessary and proper for carrying into execution the foregoing Powers, and all other Powers vested by the Constitution in the Government of the United States, or in any Department or Officer thereof."
If this can be used to make law that transfers constitutional powers between branches, it can be used to do anything whether constitutionally approved or not. This is just the empowerment clause to use their powers, including clause 11, not to use any other power that they might imagine.
Surely you were taught in school that the branches can only exercise the powers that were specifically granted to them by enumeration, and none other. 