I thought he also intended to attack Washington DC.
On the Pickett's Charge Question, this is off topic, but I read an interesting book that posited that J.E.B. Sturat's Calvary was to sweep around the Union Lines and attack the center of the Union lines from the Rear in coordination with Pickett's Charge. In fact, Stuart fired a cannon before Pickett's charge to signal that he was in position. If it had worked the Union line might have buckled. The author cited to some after mission reports where Stuart's failure to complete the mission was discussed. Unfortunately for Stuart, Custer's calvary was in his way and stopped his charge. The author states that Lee never mentioned Stuart's failure because Stuart was dead and he did not want to disparage him. Just an interesting theory.
His primary goal was to relieve pressure from Richmond and Virginia. Remember a battle, at Gettysburg, was not part of his plan, but he was forced into battle because of the North's response. Obviously when the enemy responds, plans change.
I’ve never heard that about J.E.B. Stuart. It would make more sense than Lee inexplicably sending his men up that grade/hill to die. Lee wasn’t known for sending men into a meat grinder. If so, it sounds like it was an intelligence issue, not knowing where Custer’s (7th Cav?) were.