My name sounds like a child's toy on a shelf, Joined with a fish's tool for steering itself. I live in a school but I never pass tests, I click and I whistle with air in my chest. What am I?

A soup, spell, On hearth or in oven, A vessel for warming, With family and coven.

I wear a crust but am not bread, I’m cool and sweet instead. My center’s smooth like velvet cream, At parties I’m a dessert dream.

I’m offered freely, asked or not, defended fiercely quite a lot. I may be strong, or quickly bend, depending on the mind I’m in.

It's like library but instead of checking out librs, you check out birds.