Question: Was Josh Chamberlain really given mutineers like in the movie?
Question: How did the north manage to defeat the south in the battle of Gettysburg despite a spy providing the south with information about the north during that battle?
Answer: In short, the Federal forces (who fought for the North) outlasted the Confederate army. Since it was a 3 day battle, a full explanation can not really be given here, but Lee did not actually have an accurate understanding of the Union's strength and position. While successful on Day 1, by the start of Day 2 more Federal forces arrived and the Union army had taken defensive position on the high ground. On Day 3, there was mixed communications with Confederate commanders and they did not attack as Lee had planned. The Union army was supplied with fresh forces that allowed them to hold the line. On Day 4, Lee did not attack and formed a defensive line, waiting for Meade to attack, so the Confederates could do what the Union had just done to them. But Meade never attacked and that night Lee and the Confederate troops left.
Question: James Harrison reports to general James Longstreet that the union Army of the Potomac is moving in their direction. If that is true, why didn't General Stuart report it? Stuart's mission was to report any movement by the union Army of the Potomac.
Answer: Stuart was away from the army at that critical moment. He had fallen into the trap of reading his own news press clippings about being a dashing cavalry general, and he was off trying to ride around the entire Union army in order to make headlines. His absence (and his cavalry's "eyes") kept General Robert E. Lee from making an informed decision about his army's disposition and set in motion a chain of events that probably helped lead to the Confederates defeat at Gettysburg.
Question: Why didn't General Ewell think taking the hill was practical?
Answer: Mainly because his soldiers were tired after a long march and he didn't think they could make a direct assault on an elevated position (the hill was not quite as "bare" as the film suggests). There were also reports of Union reinforcements arriving to the area, and Ewell was afraid that his army might be exposed and overwhelmed if he attempted to take the hill without assistance (Ewell had requested, and been denied, reinforcements of his own).
Answer: Yes. After the 2nd Maine Infantry was disbanded, there were 120 men with 1-year of service left. They mutinied because they said they only agreed to fight under the 2nd Maine flag and the Army disagreed. So they were marched under guard to the 20th Maine, led by Chamberlain. Chamberlain was able to convince most of them to fight, even though he was ordered to shoot any who did not fight.
Is there a reason why a few of them refused to fight?
Yes. The same reason why they mutinied.