Let's start answering your question in reverse. Ceres could not be "the missing Theia" (I know you don't say that; I'm addressing a side issue) because of its shape. If an object hit the Earth at an angle (as is currently thought), it would be pretty deformed, if it managed to stay together. If it hit the Earth head on . . . Well, it would almost certainly not survive. So if it did survive the impact, it would be in pretty bad shape. Where would such an object go? Let's investigate the idea that it went into the asteroid belt. That begs a question: Where is it today? Ceres is the largest object in the belt (and we've already ruled it out). If the object was smaller - small enough that it blended in - it would have been captured by the Earth's gravity. So its survival provides a paradox - it would have to be big to get out of Earth's orbit, but nothing that big is known. So chances are, Theia didn't survive the impact. The gravitational pull of the Earth also implies that any fragments surviving the collision would have to be moving pretty fast to escape - so fast that it seems unlikely that they stayed in a stable orbit.
Now for your belt-formation theory. It is, admittedly a very cool idea. The mass of the asteroid belt is about 4% that of the Moon - so it could be the result of the planetary crash. And some theories say that the belt is, in fact, the remains of a planet. There is, of course, one problem - the different composition of the asteroids. There are three types, differentiated by their composition - C, S, and M (their properties can be found online). So it is very unlikely that they came from the same planet.
Finally, your idea about the Earth having an orbit farther out. This one seems to have a good chance of being right. The early protoplanets in the solar system were very - very - unstable in their orbits because of the frequency of collisions. So the Earth could have been in a different orbit, and then migrated inwards or outwards.
I hope this helps.