Find the Connection

I don't have legs. I don't have arms.

I don't have ears. I live in the water.

I can swim well.

Who I am?

I am the second planet from the sun.

I spin the opposite direction as Earth.

who am I?

I am small. I have feathers.

I lay eggs. I can sing and fly.

Who I am?

 I have branches, but no fruit, trunk or leaves.

What am I?

It is purple. It is Long.

It is a softer vegetable. It grows from a plant.

What is it?