A. Washington would, no doubt, have fought to the bitter end. How many men would have fought with him, and what they would have used as weapons, is a different, and more important question. It is noteworthy that the state of arms and munitions in the Colonies was so poor that Franklin seriously proposed that the Colonial Army look into deploying LONGBOW

formations. As early as 1776 90% of Continental powder was french in origin
Well the men that were with him in 1776 and still with him in 1781 will probably stay with him until the end(despite not being paid). As far as gun powder I know early on the Continentals captured quite a lot from British convoys, raids in addition to thath received from France, Americans were also beginning to manufacture their own.
B. One battle does not make a war. The number of decisive victories by the Continental forces can be listed with little effort: Saratoga, Trenton, Princeton, Kings Mountain, Cowpens (Yorktown was a combined American/French ground force defeating a British force cut off from relief by a French naval force). Not the most awe-inspiring set of victories.
The Vietnamese didn't win a single battle and yet won the war. I remember reading about a conversation Gen. Clinton was having with I believe Knyphausen, from what I recall Knyphausen suggested that all Washington had to do was keep losing battles until you[General Clinton]ran out of men.
The Philadelphia campaign was a sideshow to the Hudson-Champlain strategy so whether the British walk to New York sail to New York or stick it out in Philadelphia(better for Washington if they do this)the strategy of dividing the colonies on aforementioned corridor had already failed(ala Saratoga).
Less undecided
D. How did you measure "will"? 1778? Von Steuben didn't even start training the Continentals until spring of '78.
Will to continue fighting which they were right up to 1783 and probably beyond if need be.
E. Philadelphia was America's SoG. The British held it, at their leisure, after defeating Washington decisively in the field. Washington then retreated to winter quarters, where, DESPITE millions in French & Spanish air, a QUARTER of his army starved to death. Now, let's imagine Valley Forge without the aid (and weapons/powder/shot) provided by France & Spain. The British were forced to withdraw by the introduction of a large French naval force into the region, until then the British had effectively cut the colonies in half.
No they held New York at their leisure, Philadelphia wasn't so easy. And I was referring to direct French and/or Spanish intervention.
F. The Southern War was brutal beyond any other part of the ARW thanks to the fact that it was almost completely neighbor vs. neighbor. The British were able to capitalize on this, taking the major cities and towns at will. Had the de Grasse not won at Virginia Capes, the Southern Strategy might just have worked. Guerilla warfare in the 1780's is more of a concept than a fact. It could irritate the British; it would NEVER have defeated them. If low intensity warfare had been decisive in the era, the French would have won their wars in North America. They didn't.
Negative, after the Battle of Guilford's Courthouse the southern campaign was effectively abandoned. Cornwallis moved into Virginia in a last ditch attempt to destroy southern resistence. Had De Grasse lost the battle of the capes Cornwallis would've been transported to New York with his army.
The United States exists because Washington understood something that may have gotten past you. His ONLY job was to keep an army in the field, fighting as rarely as necessary and only when odds (or sinking morale) forced it. Victory was to be found in Parliament, not in the field, in London shopping districts, not by taking ground. The best modern example is Giap in Viet Nam.
Exactly, see now your coming around. Its not up to Washongton to win the war, just not too lose it.