On a sunny day, does a bird or an aeroplane flying high in the sky cast its shadow on the ground? Under what circumstances can we see their shadow on the ground?

No, a bird or an aeroplane flying high in the sky cannot cast its shadow on the ground even on a sunny day because they are flying at a higher altitude where the object cannot obtain its shadow.

We can only see their shadow on the ground if they are flying very close to the ground.