With increasing annealing temperature the sharpening of the peaks indicate a growth of the crystallite size, could also be related to a relaxation of strain introduced broadening to some extend. In the small angular window you have shown it is likely impossible to distinguish between both (though size broadening is more likely the major effect here). The splitting you observe is the Cu Kalpha 1,2 splitting. At lower annealing temperatures the splitting is "masked" by the size/strain broadening. The apparent shift of the peak positions is likely related to sample preparation. I would recommend blending your sample with a lattice parameter standard to correct the apparentshift and measuring a broader angular window for size / strain separation.
It appears that Ce4+ can be reduced during heating. Forming CeO(2-x); That might explain the secondary peak. You will have to dig deeper in literature e.g. http://dx.doi.org/10.1016/0022-1902(55)80067-X