Is it possible for two planets to be going around the same orbit?

Yes, KOI-730 is a system that has just that, Some say that the dwarf planet Pluto and it's moon Charon could technically be classified at a "Dwarf binary system". So this being said from what I've gathered there are 2 ways that planets can go around a star in the same orbit. One where 2 planets share there center of gravity outside of there own so they in a sense orbit with each other around the star, the second is where to planets orbit and when one comes close to the other there gravity pull one and other to switch places and one takes the inner "sweep" while the other take the outer sweep. ( I didn't explain the second very well I really wish I had a graph to show you what I mean).
Here's a link, I hope this helps.

http://www.newscientist.com/article/dn20160-two-planets-found-sharing-one-orbit.html

The LaGrangian points are points where the forces of the other objects balance out in the same orbit. It would be eaisiest if the planets were in each other's LaGrangian points.

it's possible, but highly unlikely.
there are no examples in the observed universe
except for the satellites in geosynchronous earth orbit.

They'd be bound to collide if they were on the exact same orbit.

Yes we can see other planets.