If i moved out to live with a friend in florida without my moms approval can we get in serious trouble?

I'm not sure what "serious trouble" would be.  If your mom doesn't want you living there with your friend, she can report you as a runaway and if you are picked up by the police in Florida you could be returned to New Jersey.   If this "friend" that you are living with is someone of the opposite sex, and it meets the definition of "statutory rape" because you are underage, and the other person is over 18, the other person might be in more trouble than you. you should at the very least be in contact with your mom and let her know that you are alright.  I'm saying that as a mom, and a lawyer.