If your sander has a sufficiently strong indeed and outfield roller, you won't have any issues keeping the material flat during thickness sanding or sanding it to a consistent thickness. Reducing its thickness won't make it flatter.
My experience with ebony backs is to make them a little thinner than, say, rosewood. If the wood is well-dried - and has fully acclimatized to your shop environment - AND you make the guitar in a constant/controlled humidity environment, the 5 mm cupping won't be an issue. The back will take the arch of the braces glued to it. You will need to use a method of clamping the two halves of the back together that keeps them flat - and the gluing seam aligned - while gluing the two halves together.
As far as the cupping of the sides goes, several factors come into it. The tighter bends will be flatter across their width, the less tight bends probably cupped a bit more. Depending on how much extra width the sides have, you might be able to trim some from each edge to reduce the cupping. As for the back, thickness sanding the sides won't be an issue with strong indeed and outfield rollers to hold them flat while sanding.
Never assume that the wood you buy/receive is fully acclimated to your shop environment. Building with wood that isn't will generally bring grief.