I'm really not sure about this one, there has to be breed specific books somewhere. For the most part, I don't think as many rabbit ailments are often as breed specific as many cat and dog ones, but there are a few. In particular with rex rabbits you have to take care of their feet. Since they don't have much fur they are quite prone to sore hocks.
To the best of my knowledge, I believe that mini rexes have the dwarfing gene which may make them slightly more prone to tooth issues as well, malocclusion or overgrown roots, though I think these are more common in dwarf breeds with the extreme features such as netherland dwarf and holland lop. Mini rex don't really have the pushed in face that other dwarf breeds do. In terms of feeding, in my opinion unless you are raising for meat, or have a really specialist breed such as an angora which likely needs some additional help growing/maintaining all that fur, there's really not such a thing as a breed specific diet. All rabbits need lots of fibrous hay, all rabbits should have leafy greens, and then a small serve of daily pellets for vitamins.
You might actually have better luck getting in contact with a breed club and getting information from them, as someone who breeds mini rex should know all the ins and outs of their potential health issues.