To answers your questions
1) The NFL is split into two Leagues the AFC and the NFC for a number of reasons. Before the NFL the AFC and the NFC were competing Football Leagues. Meaning the teams in the NFC played each other and the teams in the AFC played each other. The NFC and the AFC would then crown a champion in their repective league. However under a very innovating man, Pete Rozelle, the two leagues the AFC and the NFC were merged to from the NFL. The champ from the AFC plays the champ from the NFC in the Super Bowl. However teams from both conferences also play each other during the regular season as well.
2) There are two teams that play in New Jersey, the New York Giants and the New York Jets. They play at Giant Stadium in East Rutherford NJ, confused yet?
The teams used to play in New York City, the Giants at Yankee Stadium, the Jets at the Polo Grounds however New Jersey was able to entice them to play in New Jersey at a brand new Stadium back in the 1970s they still play there today. East Rutherford, NJ (where Giant Stadium is located) is about 10 miles and 15 minutes with no traffic to New York City.
3) The Chicago Bears are from Chicago and the New England Patriots play in Foxboro.
I appreciate your interest in the NFL if you have anymore questions email me or post them here.