1. Billy Elliot is a 11-year-old boy who lives in a small town in England.
(What does 'in England' modify? Does it modify 'lives' or 'a small town'?)
2. She asks him to take ballet class.
3. She asks him to take a ballet class.
4. She asks him to take the ballet class.
(Are the three all grammatical? Which one is commonly used?)
the TOWN is in England
3 and 4 are fine; 2 is questionable.
3 means any old ballet class.
4 means a specific ballet class.
"In England" modifies town.
3 and 4 are best. A ballet class indicates any ballet class. The ballet class refers to a specific ballet class.