The exact lyrics is "Ya im out that Brooklyn, now I'm down in Tribeca" which mean that he is no longer living in brooklyn, which is a kind of poor city, and that he is now living in Tribeca which is a rich city
Shaquille O'Neal is claiming that he likes character Bullwinkle J. Moose from the 1950s/60s cartoon Rocky (a squirrel) and Bullwinkle (a moose), probably because Shaq and Bullwinkle are both large and very strong
He is saying he would do good things for you to change your life, so it will make you feel good, therefore effecting the color of the mood ring. A mood ring is a ring that changes color according to body temperature and supposedly also your mood.
a reference to the fact that Jay Z's November 25th, 2003 show at the Madison Square Garden venue in New York City to promote The Black Album sold out in less than 24 hours (on September 27th).
"suicide" doors on cars open opposite the normal direction of car doors. some people change their doors to open this way to look cool, but they were also standard on some older cars - dangerous with poor visibility when exiting (you could kill yourself).
Gale Sayers was a Hall Of Fame running back for the Chicago Bears in the '60s/'70s. He is remembered as one of the most elusive running backs to ever play the game. Ghostface is saying he is as elusive/skilled on the mic as Sayers is on the field.