It is known that the dual CFT to Schwarzschild black hole (BH) in AdS is at finite temperature and the temperature is same as the Hawking temperature of the BH. For Reissner-Nordstrom BH in AdS the dual CFT has finite matter density which is due to the charge density of the BH. Similar thing should also be true for rotating BH in AdS. But it's not intuitively very clear to me.
The Kerr/CFT duality is not yet on the level of the other dualities you mention. No-one proposes a definite CFT as the dual, it's just "some chiral CFT with a specified central charge". Also, the duality needs to be realized in the context of a proper gauge/gravity duality, in which this chiral CFT is an infrared fixed point of a UV theory perturbed by certain operators. But no-one knows what this UV theory is or what the operators are.
But someone who actually knows the subject, may know better.