Your sentences are mostly correct and well-structured, especially for a story aimed at young children! Here's a slightly improved version with minor corrections for flow and clarity:
"During the day, birds sing, a giant moose munches on grass, and little squirrels are busy looking for cones. At night, the forest changes. A lynx is out hunting to the sound of croaking frogs."
Explanation of changes:
- Changed "birds are singing" to "birds sing" — this keeps the sentence in the simple present tense, which is often used in storytelling to describe regular or habitual actions.
- Changed "is munching" to "munches" for the same reason, keeping the tense consistent.
- Kept "little squirrels are busy looking for cones" as is — present continuous fits well here, showing they are actively engaged.
- Everything else was good, so no other changes were needed.
This version keeps the language simple, fluent, and easy to understand for a 6-year-old, while being grammatically correct.