It has to be named a planet , thats all. many asteroids and comets orbit the sun, so just having a stellar orbit is not enough. As a guideline it should orbit the primary (sol), orbit in the plane of the ecliptic, not cross the orbits of other planets (ppluto an exception) and be massive.
Only by convention. Pluto would not be considered a proper planet if it were discovered today, as it is far too small, it has an eccentric orbit and it is away from the normal plane. There are various other Pluto-type rock thingies out there, like Quaoar and Sedna. The asteroids are not planets because they are too small, even though their orbit is OK. They are sometimes called "minor planets" or planetesimals or planetoids.