If the other party has an attorney I would say your chances are nil.
You already have sole custody
As often as needed. see link
Laws can vary from state to state and by case to case. A mother can get custody if she is on depression medication, but it is best to seek the advise of a lawyer.
I wouldn't know I'm just a kid.
The best way to get sample character reference letters for a child custody case is to ask the lawyer handling the case. You can also call a family court lawyer and ask them to mail you samples.
If you have any parental rights at all, I'm not sure that your ex can "leave" custody to someone else without your involvement. In any case, you need to talk to a lawyer.
One can use a custody lawyer for many reasons but the most prominent one is when one is fighting a case about a child. You can always go to your local court and seek information on current custody lawyers.
It's up to the lawyer if he wants to take your case for free.
Custody papers are not binding until a judgement has been made on your case. The lawyer may be a judge however he may not be the judge handling your case.
Legal costs for custody are varied. There are many variables to consider. Here in Ontario Canada, to start a custody case with a lawyer, you would be expected to pay $5000 as retainer to your lawyer. That is not to say that is all it will cost, depending on how long the case takes to reach an agreement, or if it goes to trial. That initial $5000 could be doubled for total costs.
Consult your lawyer immediately as you may have a case to get full custody.
Get an Immigration lawyer . You need more reason than parentage to stay. You could always go home and emigrate legally. Or have a custody case filed to bring the child to Jamaica. In any case, a lawyer would be your best bet.