Is what was done considered intentional breaking of the fast or is it under the ruling of a traveler, and what must the doer do?

Fasting is not obligatory for a child before puberty. If you have reached puberty, then repentance from smoking is obligatory because it is forbidden.

Regarding your breaking of the fast after you knew Ramadan had begun: 1. If you were a resident in the capital and broke your fast after commencing your journey, there is no sin, because a resident, after commencing a journey, is permitted to avail himself of the travel concessions. 2. If you were a resident and broke your fast before commencing your journey, you have committed a great sin, and you must repent and make up the day. 3. If you were not a resident in the capital, you are permitted to avail yourself of the travel concessions, including breaking the fast, and you must make up the day.

As for eating after arriving in the town you traveled to, there is no sin upon you, because if a traveler arrives having broken his fast during the day in Ramadan, he is not required to abstain from eating.