Do the planets revolve around the sun on the same two dimensional plane

No, they are all slightly inclined to the ecliptic. But the 8 planets in our solar system, are effectively all in orbit around the Sun in the same plane, called the ecliptic. Mercury has the most inclination at about 7 degrees.

No, they don't. If a plane can be 34.4 degrees "thick", then, the answer is yes. (YES, for the nit-pikers, I AM using Pluto's inclination to the ecliptic as the the basis for my answer.)

http://en.wikipedia.org/wiki/Inclination

Yes, the eight current planets revolve on the same plane.

Pluto, on the other hand, does not.

Pretty close but not exactly.
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No they can go all the 360 degrees around