Questions & Answers about Будучи ребёнком, она жила у моря.
Будучи is an adverbial participle from быть. In this sentence it means something like being, while being, or when she was.
So:
- Будучи ребёнком = being a child / when she was a child
This form does not change for gender or number, and it gives background information for the main action.
An important rule: the subject of будучи must be the same as the subject of the main verb. Here both refer to она.
Because after будучи, Russian normally uses the instrumental case to describe a role, identity, or state.
So:
- ребёнок = nominative
- ребёнком = instrumental
This is very common in patterns like:
- будучи студентом = being a student
- будучи врачом = being a doctor
- будучи ребёнком = being a child
So ребёнком is correct because it means in the state/role of a child.