Regardless of continuity, like Acacia Sgt said, the next game would still be the 4th installment of the series. Besides, each Chrono from the very beginning basically has started in a new dimension or timeline. I assume the next would take place in the merged one, but I could see them doing something left-field again akin to RD, taking place in an entirely new splintered reality of some kind.
As far as a DS release of CC. I just think it's unlikely. It could probably handle it graphically, but quite a bit would still have to be modified to fit the smaller screens (I know someone here mentioned before that Element grids would just look horribly tiny w/o some very serious changes made)...but lord knows there are enough characters they could give the playable axe to the forehead to save some space or w/e.
A PSP remake would just be simpler, I think, especially since it was originally released on a Sony...I don't think there are any examples of a SE game that was originally on a Sony that was remade for a Ninny. As far as "there aren't as many RPGs on PSP, so they shouldn't release it on PSP"...isn't that a little Catch-22? Besides, it's getting quite a few big name titles from SE as is: a numbered FF spin-off (Final Fantasy versus XIII), the new Parasite Eve (3rd Birthday), Kingdom Hearts: Birth by Sleep, and, of course, Dissidia (though it isn't an RPG, it IS a spin-off of 10 separate games of their most successful RPG series)...While I love the DS and know it has a lot of RPGs, many of which are great, I think the PSP has quite a few quality titles itself...and with the availability of PSN on PSP that multiplies drastically.