Since you state that Lee decided to invade the North, you already answered your first question. <g>
Check this article for your second answer.
http://www.historyofwar.org/articles/wars_american_civil_war05_invading_north.html
What side did Robert E. Lee command?
Why does Lee decide to invade the North?
3 answers
He believed that for the Confederacy to survive he needed to win a major victory on Northern soil.
Right. You can read more in that site and come up with more details.