As the other attorney suggested, do not talk to the prosecutor without an attorney. Because it is a first offense and Petit Larceny, you will likely be offered an adjournment in contemplation of dismissal ("ACD") which means you don't have to make an admission, and the case is adjourned for 6 months. If you are not re-arrested for any crime during those 6 months, the case is dismissed. That is the most likely outcome. However, you should understand that Petit Larceny is a class A misdemeanor...
If the police are involved, he was probably given an appearance ticket to appear at probation. You don't need a lawyer for that, but a parent must go with him. Often the case is settled at that point if it is a petit larceny and a first time offender. However, the department store can insist that it go forward for charges to be filed. Your child will be appointed an attorney for the child. Most know what they are doing. The attorney can ask for an Adjournment in Contimplation of Dismissal ("ACD").
It does depend on which County and the DA's there. However, it is not likely he will go to jail if he has no other priors. It is likely he will have to go to lots of counseling like MADD (Mothers Against Drunk Drivers), DDP (NYS Drunk Driver Program), TASC (Treatement Alternatives to Street Crime). He may get probation. If he has no prior DWI, it is a misdemeanor and he faces 3 years of probation and an interlock device if he has access to a car; and 6 months drivers license revocation.
I'm going to guess at what your concern is. For statutory rape, you would have to be under the age of 17 and he would have to be 4 or more years older. If your concern is trespass, e.g., if your folks told him to get off the property, you might consider dating him off premises. Otherwise, your concerns are not clear.
The other attorneys are correct in that you are still below the age of consent and your boyfriend could be prosecuted. However, for a statutory rape charge, the 2 parties have to be at least 4 years apart. He could however, be prosecuted for sexual misconduct.
Since he was given a DAT it is very unlikely he will go to jail as long as he shows up for court. If he was 15 at the time of the alleged assault, he will be charged as a juvenile delinquent. If he was 16 at the time of the alleged assault, he will be charged as an adult. The court will probably issue an order of protection for your son to stay away from the complainant. Your son will also have to sign the order of protection to show that he received a copy of it. He should have an attorney. He...
The general rule for emancipation is that the child must be financially independent, for example, if she is working and paying her own health insurance. You do still have an argument based on those facts.
I agree with all the above attorneys. Surrendering on the warrant is best. I would add these 2 points. You will not get an assigned attorney unless the traffic matter is a misdemeanor and if you qualify as far as income. If the traffic matters are simply infractions, in my experience, you will have to pay a bail of $250 for 1 ticket or $400 for 2 tickets and more for additional tickets. There will also be a "lift fee" of $75/ticket just to get the driver license suspension lifted.
You can file a petition in family court for change of custody. Generally you have to show a substantial change of circumstances showing that the best interests of the children is for them to be in your custody. You should also give thought to how to prove the children are living with their grandfolks.