A "What If" question about a planet and a sun?

Bigger and more massive are two different things. If the "planet" were so big, though, it would probably be very massive (and gaseous) nonetheless. Such a massive body (the same or greater mass than the star) would be able to initiate nuclear fusion, and thus become a star. This would form a binary star system, which are fairly common. Indeed, both stars orbit eachother.

Being bigger than a star, and not nearly as massive, however, would mean a very low density, too low for a single, distinct body anything like even a gas giant. It would essentially be a loose collection of gas and dust that is a remnant of the solar nebula, and which would coalesce to many asteroids, or into one much smaller planet, or be absorbed by the star. So, that there is a planet bigger and either less or more massive than the star makes little sense.

Still, whatever it is, the star and the planet, second star, etc. would orbit one another. Actually this is like the case for Jupiter (much smaller and less massive than the Sun). Jupiter orbits the more massive Sun, but its own gravity has a somewhat noticeable effect on the sun, causing the sun to move in a small circle.

Impossible scenario. A star is an object with enough mass that Immense pressure causes a nuclear fusion reaction to occur in the core. If there was a planet larger than its star, the fusion reaction would have started there too. And the 'planet' would be part of a binary star system. They would both revolve around a common center of gravity.

impossible. the only difference between planets and stars is that planets do not have enough mass and pressure to convert hydrogen in helium. causing them to give off light. the hydrogen is convered into helium because of the massive pressure inside the center of the celestial object, creating intense heat. this said intense heat causes the particles to move much more reapidly then they ever would on earth or any other planet. and the rapid movement causes the particles to crash together exchanging electrons, protons and neutrons, creating new atoms. so no, a planet bigger than a star is not possible. im mass perspective anyways. but in volume yes it is possible. but volume doesnt determine gravity, mass does. so volume is irrelevent in the respect of "which would orbit which" because that all depends on gravity.

Well - a planet that size would probably be a sun itself - and there are two suns in some systems - so I've heard. And apparently they revolve around each other.

if this "planet" had a gravitational field to equal it's size, then yes, the sun (and the rest of the solar system for that matter) probably would revolve around it

yes, although it's basicalyl impossible for a planet that size to not begin fusion

maybe because it still has strong gravity

Anything is possible.