Yes, there are several probes that could (and those that are still active can) see that region of space. Plus any spacecraft that left Earth-Moon system, and had capabilities to take photos as it flew to other planets in the Solar system (or to the Sun itself).

No, there isn't anything there. Several reasons. L3 Lagrange point of Sun-Earth system is there. L3 is unstable point, nothing could hide there for very long, it'd fall out of orbit relatively quickly. Earth is a planet, meaning its gravitational influence is strong enough to clear its orbit of other stuff. This includes stuff attempting to orbit on the opposite side of the Sun from us. I.e. anything in Earth's orbit either gets stuck in one of the two stable Lagrange points (L4 and L5; there's some dust and couple of asteroids stuck there), captured into orbit around Earth (becoming a moon, but so far no luck for capturing that 2nd moon), or eventually flung out.

And as several people mentioned already, even without being able to see, we'd be able to detect gravitational influence of anything sufficiently large, like another planet. In case you were asking if there could be something large (e.g. planet sized) hiding there, the answer is resounding no. Even if there could be something large out there (which it can't, orbital mechanics simply doesn't allow it), we'd figure it out back in the 19th century by simply observing trajectories of other stuff that we can see, long before we started launching stuff in space.