Most birds that nest in holes and hollows, such as owls, woodpeckers, parrots and toucans lay white eggs. So do the huge majority of pigeons/doves. But there are plenty of other birds that do as well, such as many species of waterfowl.
A white-breasted Nuthatch might be the bird you're looking for.
Its a Robin but it could also be cardinal or many others.
A swallow is a small bird.
Robins lay small blue eggs with little spots.
The type of eggs you would see will depend on where you are. If you are on a farm, you might see chicken eggs. If you are around lakes and streams, you might see fish eggs, turtle eggs, or the eggs of other amphibians.
Sounds like a humming bird.
the white bird
A white-breasted Nuthatch might be the bird you're looking for.
some fish do.
A male bird!
The bird that can fly with white wings is the white dove.
A killdeer lays these eggs but they can sometimes be blue with brown spots
A baby bird is called a chick. A kind of small bird is a hummingbird.
I'm pretty sure it's a penguin.
brown and white
The bird with a blue and white tail is called a blue jay.
Yes, they will eat bird eggs and any kind of nestling bird.