I hope it's OK to answer an old question.
First, let me say that your proposal is creative. You've explained the possible creation of the asteroid belt (by collision - not impossible), and you've combined it with the formation of the moon by impact. That 2nd part is a little more problematic.
There's a principal in scientific theory and it applies to astronomy that as you add requirements to a scenario, the probability decreases significantly. (I don't know if there's a name for that principal but I've read it, I'm not making it up).
Earth was once outside of Mars.
Earth was struck by a large object creating the Moon
That impact blew off matter which became the asteroid belt
The impacting object may have become Ceres
The impact pushed the Earth into a lower orbit.
That's a LOT of events strung together, which raises the improbability of your scenario. That's not to say it's impossible, and improbable things can happen, but you need a LOT to fall into place for the theory to work.
Could Earth have once been outside Mars? Sure, theoretically. Planets have been known to migrate, though how common this is isn't well understood and if Earth and Mars passed close to each other, Earth could have given Mars a kick outwards. It's possible that the inner 4 planets may have swapped orbital positions in the past.
The giant impact that created the Moon is an accepted theory, though there's some variation on the precise mechanism, it's generally accepted and it explains a few things like the similarity of isotopes and nearly identical age of the Earth and Moon and the high angular momentum of the system and the Moon's very large relative size. This part of your model is strong.
The impact blew off debris that became asteroids - I've not seen any mathematical models for how much debris could have been blown outside the gravity well when the giant impact happened, but if I was to guess, I think it's very reasonable that the giant impact left a debris field of asteroids as a result of the impact.
Theia became Ceres. - This is a problem, because the material that makes up planets behaves like a liquid when they smash together. If it had been a glancing blow, then maybe, but there's the problem that the moon is much more massive than Ceres. A glancing blow wouldn't create a larger collection of debris and leave a comparatively tiny impactor. The Moon is like 70 times the mass of Ceres, so that just doesn't work.
Now if you'd said Mercury may have been the impactor and Mercury had a glancing blow, in the process, Mercury losing much of it's outer shell as it nicked the Earth - creating the Moon in the process, it would still be unlikely but at least the masses would work. Mercury could in theory, set the Earth spinning and in the collision lose a lot of it's outer material. I'm not saying that happened, only that the mass of mercury is close to what you'd need to set the Earth/moon system spinning so fast.
It's generally assumed that Theia was absorbed and completely destroyed in the impact, but a glancing blow by Theia becoming Mercury .... just maybe.
The Earth's orbit changed - this is also a problem. With any giant impact, some of the energy is lost in debris flying away and some is converted to heat and angular momentum, but generally speaking, momentum is still concerved. In other words, to slow the Eareth down and drop it into a lower orbit, the two objects would need to be moving in different orbits, that is, the smaller object (Theia) would need to be orbiting the wrong way around the sun. While that is possible (perhaps from a gravity assist around Jupiter), it's unlikely. What's more, opposite orbits greatly increases the speed of impact, so for the Earth to survive, you need to decrease the Mass of Theia if you increase the velocity of impact.
An impact changing Earth's orbit would send Earth into a more eccentric orbit, which then could theoretically interact with Mars and circularize over time, but the idea of a planetoid with a wrong way orbit hitting Earth increases the improbability.
Don't get me wrong. I like where your theory is coming from. It's just when the details are examined, it appears improbable.
That said, as asteroids in the belt are examined, if a number of them are shown to have earth and moon like isotope ratios, that might lend support to aspects of your proposal, though Ceres having once been Theia is highly unlikely, both because it's too small and Theia is believed to have not survived and because Ceres has an enormous amount of water. Ceres is more like an outer solar-system object, like a formation moon of one of the outer planets or a dwarf planet in the Kuiper belt, that by some mechanism, probably a gravity assist, may have migrated inwards.
Keep coming up with theories. I like your approach.