Would i need a permission letter to fly out of country? (divorce-related)?

The answer depends on the details in your parents' divorce decree. Since your dad lives in a different country, I am pretty sure your parents anticipated out of country travel and probably have some specific stipulations on how and why it can occur. You will definitely need to get a passport. This will require sending in your birth certificate or a certified copy of it. Whoever holds that document (probably your mother), determines how willing they are to cooperate in the process (i.e. if your mom doesn't want you to visit your dad, she will probably withhold your birth cert so you can't get a passport). Sounds like your parents should be communicating about all of this.

Your question has nothing to do with airport personnel. It has to do with the fact that if your mother does not get permission either from your dad, OR from the courts first, she can be arrested for taking you out of country. Let your parents handle this.