Letter of Consent to travel and custody of 12 yo

Hi all,

I've read through all the posts but still need some advice about my situation. I have never been married to the mother of our 12 yo son, so we don't have any divorce agreement but have lived with him since he was born together with the mother now we are splitting up. My name is on both his Thai and US birth certificates, I am legitimized as the father from the Banglamung Ampur a couple months ago, he has both Thai and US passports. The mother agrees to give me custody and take full responsibility of our son.

Question 1: Is it possible for her to go back to the Ampur and sign some sort of open ended consent letter stating that I can take our son abroad to visit or live at any time in the future or do we need a separate letter for each time we travel? 

Question 2: Is it possible for her to sign over parental rights or full custody to me at the Ampur or is it required to go through the court system.

Many thanks for any advice on this subject especially if anyone has been through this same scenario as most of the posts that I've read deal with custody after divorce with divorce agreements involved.