Learn Finnish: Lapsi käyttäytyy hyvin koulussa. - The child behaves well at school.

It is derived from the verb käyttää (to use). By adding the reflexive suffix -ytyä, the action is directed at the subject itself. Literally, it translates to 'using oneself' or 'carrying oneself', which naturally evolves into the meaning 'to behave'.

Why does the suffix take the form -ytyä instead of -utua in this word?

Finnish vowel harmony dictates that words containing front vowels (y, ä, ö) must take suffixes with front vowels. Since the root käyttää contains front vowels, the suffix matches it and becomes -ytyä.

Is there a reason we use the inessive case (koulussa) for 'at school' instead of the adessive (koululla)?

Yes. For institutions like school, Finnish uses the inessive case (-ssa) to refer to being 'at school' in the sense of attending it or being actively involved in its environment. If you used koululla, it would strictly emphasize being physically present outside or around the school building.

Why does the sentence use hyvin instead of hyvä?

Hyvin is the adverb form of the adjective hyvä (good). Because it modifies the verb käyttäytyy to describe how the child behaves, you must use the adverb form, meaning 'well'.