Can there be another planet in our solar system in the same orbit as earth but on the opposite side of the sun? We would never see it because it would always be behind the sun.

It turns out that such an orbit is unstable in the sense that if you put a planet (or any object) there, any small nudge would cause it to move far away from the point directly opposite Earth. It's very similar to trying to stand a pencil on its top: if the pencil isn't _exactly_ vertical, it will quickly fall over.