When a Product Owner creates a story, as well as acceptance criteria, what needs to happen if the team decides to break down the story? Should the team decide on the acceptance criteria, as long as the acceptance criteria of the main story are met?
What if the new stories that are created after breaking down the main story are purely technical?
The simple answer to this questions is you add acceptance criteria if you find them useful.
This is not a procedural thing. The idea of acceptance criteria came about because teams found them useful when it came to implementing stories. If you find acceptance criteria useful on stories that you have broken down from larger stories then use them.
What if the new stories that are created after breaking down the main story are purely technical?
Well then they are no longer stories, they are technical tasks.
A user story is a requirement described from the point of view of an end-user of the feature.
It is a common practice among Scrum teams to break stories down in to one or more technical tasks during sprint planning.