10. Assume for a moment that Pickett's charge at Gettysburg works and the Rebels win there. Would it be entirely possible to have seen a major battle and possible bloodbath in Philadelphia or Baltimore? (Something that would have possibly dwarfed the casualties and deaths at Shiloh, Antietam, etc.?)
Gettysburg was lost before Pickett ever made that charge. Desperate times call for desperate measures, which Pickett's charge was. But leaving that aside and taking the second part of the question, Lee would have had a choice: Proceed North East to Philadelphia, as you suggest, or two round back South easterly towards Washington DC (as you suggest in #8). To proceed towards Philadelphia would leave his line of support to be too long, too weak and subject to attack.
He would have attempted to block off DC, and possibly lay siege to it. A siege though would be time consuming and the North would be in a better position to defend DC (they controlled the waterways).
I believe he would have used the momentum of a victory at Gettysburg to directly attack DC and force a surrender. He simultaneously would have sent raiding parties off in multiple directions to bring the war home to the north, cgathering supplies and forage while doing so.
Even winning at Gettysburg though is no guarantee of a southern victory in the war.
It couldn't have have brought about a truly military victory in any case -- by that time the Confederacy would not have been able to sustain the sort of offensive necessary to reach DC, for the same reasons you give for them reaching Philadelphia.
Confederate hopes for victory at Gettysburg would have depended on its impact to Union morale, and the war-weariness that would result from the expensive effort that would have been needed to oust them from the Gettysburg area.