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Does the War Powers Act does give POTUS the power to wield the military any way he pleases, any time he pleases?

No it does not. The War Powers Act does NOT give POTUS the power to wield the military any way he pleases, any time he pleases. 
Section 1541: (c) Presidential executive power as Commander-in-Chief; limitation

The constitutional powers of the President as Commander-in-Chief to introduce United States Armed Forces into hostilities, or into situations where imminent involvement in hostilities is clearly indicated by the circumstances, are exercised only pursuant to:

(1) a declaration of war,

(2) specific statutory authorization, or

(3) a national emergency created by attack upon the United States, its territories or possessions, or its armed forces.